## 1. Introduction

Even though differential reflectivity

There are several other techniques that have been used for the calibration of

Another technique uses the principle of radar reciprocity that states that the two cross-polar backscatter cross sections are equal (Saxon 1955; Hubbert et al. 2003). This has been termed the cross-polar power (CP) technique, which uses the integrated ratios of the two CP powers, along with solar measurements, to calculate a

To analyze the time variability of the

As a practical note, what is the accuracy of

### Uncertainty

No matter how meticulously any measurement is made, there is a degree of error or uncertainty (Taylor and Kuyatt 1994). In part, this paper addresses and attempts to estimate what the uncertainties are for the CP and VP *σ*, which represents the random error. This assumes that there is a calibration measurement reference; that is, we know what the true mean value should be. It is also assumed that the repeated measurements are executed over a period during which the device under test (i.e., the radar) is in a stable state. This means that the state of the radar—that is, the transmit power and the gains—are consistent to within the precision of the desired calibration characterization. Knowledge of the time stability of the *k* times the standard deviation of the random error, where *k* defines confidence or “coverage” demanded by the users of the specification. It is widely thought that

There can be subtle systematic bias present due to data processing techniques and other radar system factors that are not revealed by repeated measurements. For example, one reason why the engineering calibration technique produces unacceptably large uncertainties is that the external power measurement introduces systematic errors (Hubbert et al. 2008a). Also, it has been assumed that VP data integrated over several 360° rotations of the antenna will yield 0-dB

In this paper, we use the CP technique for investigating the variability of

Experimental data from NCAR’s S-Pol radar are used to illustrate the theory. Of particular interest to the scientific community, we use data from the recent Plains Elevated Convection at Night (PECAN) (Geerts et al. 2017) field campaign to demonstrate the CP technique.

This paper is organized as follows. Section 2 gives a description of S-Pol and theory for the CP technique. In section 3, the temperature dependence of

## 2. The CP calibration technique for S-Pol

The CP method has been successfully applied to the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) radar and S-Pol data to calibrate

Shown in Fig. 3 is a simplified block diagram of S-Pol that captures the essential radar components. The term

S-Pol uses a single transmitter and a fast mechanical polarization switch to transmit alternate pulses of H and V polarization (termed FHV mode). Because of the IF transfer switch, there are four possible paths through the receiver chain. S-Pol uses the IF switch so that the copolar (and cross polar) signals always use the same receiver path from the IF switch to the in-phase and quadrature (I and Q) samples; that is, S-Pol uses copolar and cross-polar receivers instead of H and V receivers. This is done so that errors in

### a. Cross-polar power technique: Data collection

Execution of the CP technique requires two measurements: 1) solar scans and 2) cross-polar power measurements. Solar scan data have been described and shown before in Hubbert et al. (2010).

#### 1) Solar measurement

Solar radiation at S band is assumed unpolarized and thus the H and V powers are equal. During high sunspot activity, there can be circularly polarized radiation (Tapping 2001). However, circularly polarized radiation will split equally into H and V polarized components and thus we assume that such solar activity will not bias our measurements significantly. The sun is scanned within a box that is approximately ^{-1}. The radar scanning software tracks the sun and automatically changes the scanning limits so that the center of the sun is maintained in the center of the scanning box. A total of 128 H and V samples are integrated per point, and the power samples are corrected for background noise. The noise can be calculated while the radar is pointing away from the sun during the solar box scan. Upon completion of the box scan, the data are interpolated to a

#### 2) CPR measurement

For FHV operations the CP power ratio can be calculated from either weather or clutter targets and is typically an average of hundreds or thousands of measured cross-polar power ratios from a PPI scan or an entire volume scan. The CP technique takes advantage of the principle of radar reciprocity, which applies to the entire radar antenna pattern so that power transmitted and received through the antenna sidelobes does not bias the measurement. For the following datasets, S-Pol was in FHV mode with a pulse repetition time (PRT) of 1 ms. Thus, a cross-polar power pair, separated by 1 ms, comes from nearly the identical resolution volume of scatterers, since neither they nor the antenna moves appreciably in 1 ms. To ensure good data quality, several thresholds are used for the CP powers: 20 dB*ratios* that pass this criterion are then averaged over the input dataset. For FHV operations, a single low-level PPI scan can yield sufficient data for an accurate (uncertainty less than 0.05 dB) estimate of CPR.

## 3. bias as a function of ambient temperature

In this section a

### a. The MASCRAD dataset

During December 2014 through March 2015, S-Pol was located at its Front Range Observational Network Testbed (FRONT) field site near Firestone, Colorado, and gathered data for MASCRAD. For calibration purposes, many solar scans were made over a wide range of temperatures that proved advantageous in detecting a relationship between

Figure 4 shows an example S-Pol time series of

Examine

Other possible sources of

Thus, it has now been shown that the radar components in the complete receive path (from the reference plane through the receivers) cause relatively little

*necessary that the transmitter be on*during solar scans or else a bias will be incurred. It was found that the circulators’ H-to-V differential gain changes when there is no high-power pulse passed through them. Shown in Fig. 9 is a scatterplot of the 328

*T*is the temperature (°C). The Pearson linear coefficient of correlation is 0.902. The conclusion is that the variation in

To visually demonstrate how temperature affects the

### b. Measurements during PECAN

From 1 June to 15 July 2015, S-Pol collected data for the field campaign PECAN, which was centered at Hays, Kansas. S-Pol was located about 26 mi southeast of Hays, close to McCracken, Kansas. During the initial part of PECAN, S-Pol suffered several mechanical failures, such as the rotary joint, transmitter, and air conditioners. The S-Pol system did not achieve stability until 16 June and thus the data given below are restricted to 16 June–16 July.

*T*is in degrees Celsius. The Pearson linear coefficient of correlation is

^{-1},whereas the slope of the line in Fig. 9 is positive 0.0082 dB °

To illustrate the long-term nature of the abovementioned

Figure 13 shows a scatterplot of low-pass filtered time series of CPR versus low-pass filtered time series of

Since the state of S-Pol was quite stable from 16 June to 16 July, the regression curve from Fig. 11 can be used to estimate *σ* uncertainty of 0.04 dB. The temperature of S-Pol’s antenna is known (measured in 10-min intervals). CPR is estimated from both PPI and RHI scans over the entire measurement period and this provides about 6-min temporal resolution for CPR. Under these conditions,

## 4. bias from vertical-pointing data

To support the CP

Comparison of

The 2 July VP measurements present an interesting 50-min-long case, during which there was a 4.7°C drop. Figure 16 shows a comparison of VP-measured and CP-estimated

## 5. Uncertainty analysis

### a. CP technique

To estimate the uncertainty of the CP technique *σ* is 0.0084 dB, which is considered the uncertainty of the *σ* confidence level. Similar measurement errors were determined from other days during MASCRAD and PECAN.

Next, the uncertainty of CPR is addressed. Figure 18 shows a scatterplot of the cross-polar powers *m* on the *x* axis. For cross-polar power from *m*, the mean trend in CPR is about constant at an average of approximately

To estimate the uncertainty of the mean CPR from the abovementioned volume of data, bootstrap resampling is employed (Efron and Tibshirani 1998). There are 12 303 CPR values, and this dataset is resampled with replacements to create a dataset with 10 000 values. The mean of the resampled dataset is then calculated. This process is repeated 10 000 times and the mean of the means is

The uncertainty of the CPR estimate can also be found from the time series of CPR calculated from RHI and PPI volume data collected during PECAN. Figure 20 shows those CPR estimates from 21 June to 16 July (one estimate per volume scan). The red curve is a low-pass filtered version of the raw black curve and it represents the mean trend of CPR. The diurnal oscillations are primarily due to fluctuations in the transmit power ratio, which in turn are likely due to temperature oscillations inside the transmitter sea container. The difference of the two curves yields a standard deviation of 0.004 09 dB, which is an estimate of the measurement uncertainty. This compares very well with the uncertainty estimate of 0.003 48 dB calculated from bootstrap resampling mentioned above. Below the uncertainty from the bootstrap technique is used.

The *σ* level and 0.0408 dB at the 2*σ* level.

### b. VP technique

To estimate the uncertainty of the VP

To further illustrate the uncertainty of the VP

These uncertainty estimates assume that there are no undetected systematic biases. For example, if the shape of the antenna were to change from when it points horizontally to when it points vertically, then the vertical-pointing

## 6. bias estimation from Bragg scatter

In this section the

To identify Bragg scatter, the following thresholds are used:

- the resolution volume is identified as “cloud drops” by the particle identification (PID)
^{1}algorithm - 4 km
range 30 km - reflectivity
0 dB *Z* - 3 dB
SNR 50 dB 0.98 (no noise correction) radial velocity 1.5 m s ^{-1}

Stronger Bragg scatter events are manually identified that are large in spatial extent and continuity in the high *σ* uncertainty of the

Figure 24 shows a comparison of the 0000 UTC 21 June Bragg data with curve A calibrated using the regression curve from Fig. 23 and curve B calibrated using the regression curve from Fig. 11. Since Bragg scatter should have 0-dB

## 7. Possible cause of the bias temperature sensitivity

The cause of the temperature-dependent *μ*cm^{−1} cm^{−1} (°C)^{−1}. The S-Pol support struts are about 18 ft (243.8 cm) long, so for a change of 10°C this translates to an expansion of 1.30 mm, which is of the same order of magnitude as 1.37 mm. While this is not proof that the thermal expansion of the S-Pol antenna is the cause of the

## 8. Summary and conclusions

This paper has presented a detailed analysis of ^{-1} and for PECAN data ^{-1} as determine from regression fits of

To corroborate the CP

The uncertainty of the CP *σ* (95% confidence) level. Such low uncertainty is contingent upon the algorithm used, the data quality of the radar, the stability of the radar, and the diligence of the radar staff. This uncertainty can be considered valid for a snapshot measurement of the calibration state of the radar and may be good for only a few tens of minutes as it was for S-Pol when the ambient temperature was rapidly changing. For S-Pol, it was possible to derive a *σ* level.

It is shown in appendix B, using experimental data, that the CP technique can be successfully applied to SHV radars. The mean CPR estimates from FHV data and SHV data were nearly identical. A radar transmit circuit was illustrated that would support CP

Next, the data from Fig. 2, which in part motivated the research for this paper, are revisited. The ^{-1}. This is nearly identical to the slope of the regression fit for ^{-1}. Thus, it is apparent that S-Pol’s

It is likely that all weather radars with center-fed parabolic reflector antennas experience the temperature-dependent ^{-1} for S-Pol operating at 2809 MHz, and the nature of this temperature dependence is likely to change for different operating frequencies. Depending upon the application, this amount of

This work was supported in part by the Radar Operations Center (ROC) of Norman, Oklahoma (EOL-2017-0711). The author would like to acknowledge the EOL/RSF technical staff for its time, effort, and interest in the collection of the experimental data used in this paper. In particular, Dr. Michael Dixon designed and wrote the solar scan and CPR analysis software and provided valuable technical discussions. The author also acknowledges Richard Ice, who recently retired from the ROC, and Frank Pratte, a former engineer at NCAR, both of whom have provided many helpful technical discussions and insights over the years. The helpful comments of three anonymous reviewers, which greatly improved the manuscript, are appreciated. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the National Science Foundation.

# APPENDIX A

## Derivation of the CP Technique for Calibration

*s*” denotes a solar measurement. To calibrate

In this derivation any cross coupling effects are neglected. S-Pol’s cross coupling is assessed from examining

# APPENDIX B

## Using the CP Technique for Calibrating SHV Radars

One technique for the evaluation of CPR is to alternate between only-H and only-V transmission on a PPI-to-PPI basis. If the beams are indexed, then cross-polar powers from the same resolution volumes (but from different PPI scans) can be paired and used for the CP

The question to be addressed is, can the CPR be calculated accurately from H and V samples that are separated in time on the order of a minute? Such SHV data can be simulated from FHV data. The H-polarization data from one FHV PPI scan can be compared to the V-polarization data from the next FHV PPI scan; the SHV CPR can be calculated and then compared to the equivalent FHV CPR from the same data.

On 19 April 2011, a consecutive series of thirty-four

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^{1}

PID is the NCAR-developed echo classification algorithm (Vivekanandan et al. 1999).