# Looking for References for R(KDP) Power Law Coefficients in \_coeff\_rkdp\_table() (Py-ART)

**URL:** <https://openradar.discourse.group/t/looking-for-references-for-r-kdp-power-law-coefficients-in-coeff-rkdp-table-py-art/626>\
**Category:** General\
**Tags:** py-art\
**Created:** [July 18, 2025, 8:30pm UTC](https://openradar.discourse.group/t/looking-for-references-for-r-kdp-power-law-coefficients-in-coeff-rkdp-table-py-art/626 "2025-07-18T20:30:07Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![eltonrobaina](https://yyz2.discourse-cdn.com/free1/user_avatar/openradar.discourse.group/eltonrobaina/32/13_2.png) [@eltonrobaina](https://openradar.discourse.group/u/eltonrobaina)\
**Post date:** [July 18, 2025, 8:30pm UTC](https://openradar.discourse.group/t/looking-for-references-for-r-kdp-power-law-coefficients-in-coeff-rkdp-table-py-art/626/1 "2025-07-18T20:30:07Z")

</div>

Dear Open Radar community,

I am currently investigating the **R(KDP) power-law relationships** used in the `pyart.retrieve.qpe` module from the Py-ART library and would like to ask for your help in identifying the **original references** that support the coefficients defined in the internal function `_coeff_rkdp_table()`:

def \_coeff\_rkdp\_table():  
coeff\_rkdp\_dict = dict()

```
# S band: Beard and Chuang coefficients
coeff_rkdp_dict.update({"S": (50.70, 0.8500)})

# C band: Beard and Chuang coefficients
coeff_rkdp_dict.update({"C": (29.70, 0.8500)})

# X band: Brandes coefficients
coeff_rkdp_dict.update({"X": (15.81, 0.7992)})

return coeff_rkdp_dict

```

These values are used in the generalized power-law equation:

R=aKDPb

However, despite comments in the code stating that the S- and C-band coefficients come from Beard and Chuang, and the X-band coefficients from Brandes, I have been unable to locate these articles.

In particular, I am looking for the source (preferably peer-reviewed) that supports:

- **S band** : (50.70, 0.8500)
- **C band** : (29.70, 0.8500)
- **X band** : (15.81, 0.7992)

Do these coefficients come from published literature, or were they empirically derived from specific datasets (e.g., U.S. mid-latitude stratiform/convective events, ARM campaigns, etc.)?

Any help in tracing back the original references for these values would be greatly appreciated.

Best regards,  
**Elton J. Robaina da Silva**