**1. Introduction**

Rainfall plays a critical role in the earth's water and energy cycle over a wide range of spatiotemporal scales. Therefore, accurate quantitative estimation of rainfall is an important input for engineering design applications where Precipitation Frequency Estimates (PFE) are highly sought [1]. The purpose of a precipitation frequency analysis is to determine the frequency at which certain intensities or depths of precipitation are expected to occur. Probabilistic modeling and statistical analysis techniques of extreme rainfall are used to provide PFE information and characterize the relationships between three important precipitation variables: intensity (or depth), duration, and frequency [2]. Such relationships are usually referred to as Intensity-Duration-Frequency (IDF) or Depth-Duration-Frequency (DDF) curves. Statistics derived from IDF or DDF curves are typically used

to develop design storms, which are then used as an input for a variety of engineering applications such as design of dams, levees, reservoirs, and urban sewer systems [3].

Precipitation frequencies are typically estimated using sparse gauge observations. The evolution of weather radars allows the spatially continuous estimation of rainfall at small temporal sampling intervals, thereby filling the observational gap of rain gauges in space and time. Radar does not measure surface rainfall directly; instead, it measures the backscattered power from the hydrometeors aloft and the received power is then converted into rainfall estimates with inherent errors. The availability of NEXRAD Quantitative Precipitation Estimates (QPE) in high temporal and spatial resolutions covering the United States (US) has motivated researchers to study the applicability of the radar-based QPE in deriving precipitation frequencies [4–8]. For instance, Overeem, et al. [8] used radar data covering the entire land surface of the Netherlands for a 10-year period (1998–2008) to derive radar-based areal reduction factors (ARFs), which were found comparable to those based on high-density rain gauge networks and thus concluded that radar data, after careful quality control, are suitable to estimate extreme areal rainfall depths.

For sites that sufficiently have long records with respect to the return period of the extreme precipitation quantile of interest, at-site frequency analysis can be an adequate approach. However, for un-gauged sites, or for sites with historical records that are too short to make a reliable prediction of extreme quantiles, data augmentation from neighboring sites is needed. Thus, two main approaches for the frequency analysis have been discussed in the literature. The first is an at-site estimation approach, which simply uses data at each station, while the second method is a regional estimation approach that makes use of observations from gauges sharing a homogenous region with similar climatological and physical characteristics [9–14]. Svensson & Jones [13] reviewed the different estimation methods of rainfall frequency analysis in nine countries and reported that, while each country's method is different, most of them use some form of regionalization to transfer information from surrounding sites to the target location. A regionalization method combines a local estimate of an index variable (typically the mean or median annual maximum rainfall) with a regionally derived growth curve to obtain a design rainfall estimate. Naghavi & Yu [15] applied a regional frequency approach to precipitation data in Louisiana using Annual Maximum Series (AMS) extracted from 25 synthesized stations with long periods of record. The results showed that the regional approach can substantially reduce the relative root-mean-square error (RRMSE) and the relative bias (RBIAS) in precipitation quantile prediction.

Although radar QPE can provide site (pixel)-specific PFEs with a high spatial resolution, regionalization techniques could be advantageous to reduce the sampling variability in the radar PFEs [4,6,16]. Eldardiry et al. [16] tested three regional estimation procedures and indicated lower uncertainty bounds associated with regional approaches compared to pixel-based PFEs. However, they also reported on the effect of the relatively short radar records on the uncertainty associated with the radar-based quantiles. Using QPE data during 1993–2000 over the Arkansas-Red Basin River Forecast Center (ABRFC), Durrans et al. [4] concluded that data heterogeneities and the temporally-limited data records are major factors that hinder the development of depth-area relationships using radar-rainfall data.

In this study, we assess the robustness of a probability weighted regional spatial bootstrap approach to estimate precipitation frequencies using radar data. This method was proposed by Uboldi et al. [17] as a resampling approach for estimation of parameters of rainfall annual maximum series statistical distribution. Using the regional spatial bootstrap technique, we investigate two main issues that impact the use of radar-based QPE in deriving precipitation frequency estimates: (1) the typically short historical records of radar-based QPEs; and (2) the effect of outliers in precipitation maxima series that could possibly cause unrealistic spatial gradients in IDF relations. We assess the utility of the spatial bootstrap approach in alleviating such limitations and compare the PFEs from the regional bootstrap approach against estimates derived using an at-site (pixel-based) method and PFEs reported in a US gauge-based Precipitation-Frequency Atlas [18]. The study is performed using radar-based QPEs over the state of Louisiana, USA.

#### **2. Datasets and Methods**
