Attributing the Variability of Hershfield Rainfall Sampling Adjustment Factors at Sub-Hourly Durations
Authors: Meier Claudio , Muñoz-Proboste Patricio , Marasini Apeksha , Kafle Nischal , Dell'Aira Francesco 
Published: March 2024

Engineers and scientists need to describe extreme precipitation at a location. For any duration of interest, IDFs (or DDFs) represent the rainfall that can be expected to be equalled or exceeded with a certain frequency. In urban drainage, for durations ranging from a few minutes to a few hours, DDFs must be derived analyzing maxima obtained from &#8220;continuously measuring&#8221; raingauges. However, most rainfall records are not truly continuous, but are instead totalized. As we cannot know the actual maxima in continuous time for those shorter rainfall durations similar to gauge resolution, we introduce a negative bias. Only recently, within the last 10 to 15 years at most, meteorological agencies in developed countries have widely installed raingauges with 1-min resolution, which are basically continuous. This means that the DDFs that we presently use all came from totalized data. How were these biased, &#8220;fixed maxima&#8221; converted into values that are closer to the actual, unconstrained maxima?&#160;The traditional solution has been to use so-called rainfall sampling adjustment factors (SAFs), also referred to as Hershfield factors. These multiplicative correction factors can be derived at raingauges with higher temporal resolution, so that maxima can be extracted using sliding time windows which are closer to continuous, allowing for comparison with maxima extracted from the same data, but totalized. Typically, such SAFs are assumed to be applicable at other locations, or even universally. The constrained maxima extracted from totalized data are simply multiplied by a SAF in order to obtain their corresponding unconstrained equivalents, which are considered to be the actual, continuous maxima, that are then used to determine DDFs.&#160;We found several important issues and research gaps with the way we determine and apply SAFs in current practice: (i) different authors have used varied procedures to compute them, without comparing or discussing, (ii) no one has looked at the variability of SAFs at a given location, and (iii) SAFs are determined as a mean or central tendency value, across multiple locations, without considering their variability and how it affects the resulting predictions of extreme rainfall.&#160;We use 862 German stations and 147 ASOS US stations, with 1-min rainfall data, to perform a detailed analysis of rainfall SAFs. Our aims are to compare the different procedures that have been proposed, study SAF variability both at a station and in space, and propose a unified engineering methodology for dealing with totalization effects on extreme rainfall estimation. As the 1-min records are short (10 to 15 years), we use partial duration series to compute the rainfall quantiles, restricting our work to low and intermediate ARIs, avoiding estimation issues.&#160;Our results suggest that: (i) there is a preferred procedure for computing SAFs that should be adhered to, (ii) at-a-station variability of SAFs is large enough to be relevant for engineering design considerations, (iii) SAFs display spatial structure, and (iv) all of these findings should be studied in different regions, and consistently incorporated into engineering practice.