Temporal changes in rainfall intensity-duration thresholds for post-wildfire flash floods and sensitivity to spatiotemporal distributions of rainfall

Abstract. Rainfall intensity-duration (ID) thresholds are commonly used to assess flash flood potential downstream of burned watersheds. High-intensity and/or long-duration rainfall is required to generate flash floods as landscapes recover from fire, but there is little guidance on how thresholds change as a function of time since burning. Here, we force a hydrologic model with radar-derived precipitation to estimate ID thresholds for post-fire flash floods in a 41.5 km2 watershed in southern California, USA. Prior work in this study area constrains temporal changes in hydrologic model parameters, allowing us to estimate temporal changes in ID thresholds. Results indicate that ID thresholds increase by more than a factor of 2 from post-fire year 1 to post-fire year 5. Thresholds based on averaging rainfall intensity over durations of 30–60 minutes perform better than those that average rainfall intensity over shorter time intervals. Moreover, thresholds based on the 75th percentile of radar-derived rainfall intensity over the watershed perform better than thresholds based on the 25th or 50th percentile of rainfall intensity. Results demonstrate how hydrologic models can be used to estimate changes in ID thresholds following disturbance and provide guidance on the rainfall metrics that are best suited for predicting post-fire flash floods.



Introduction
Heightened hydrologic responses are common within and downstream of recently burned areas, resulting in an increased 23 likelihood of flash floods. Rainfall intensity-duration (ID) thresholds are commonly used to assess the potential for flash floods 24 ( . Post-fire debris flows, however, tend to initiate in small (<1 km 2 ), steep watersheds. In these small 67 watersheds, the rainfall intensity responsible for initiating a debris flow can be characterized by a single rain gage installed 68 near the initiation zone. Flash floods differ in that they tend to occur at larger spatial scales where rainfall is spatially variable 69 and may not be adequately characterized by data from a single rain gage. Radar-derived precipitation estimates, which can 70 provide high spatiotemporal resolution of rainfall intensity, present opportunities to develop basin-specific thresholds for post-71 fire flash floods. However, high spatiotemporal variability in rainfall intensity also brings new challenges when employing 72 radar-derived precipitation in flood warning practice. In particular, what is the best way to summarize spatially and temporally 73 variable rainfall intensity information with a single metric that can be used as a threshold? How does hydrological recovery 74 following fire influence the generation of flash floods and the metrics that are best suited for their prediction? Data-driven 75 approaches to answering these and related questions may be hampered by limited monitoring of post-fire hydrologic response 76 throughout the recovery period and the stochastic occurrence of rainfall over burned areas, which limits opportunities for 77 observations. Given a well-constrained hydrologic model that accounts for changes associated with post-fire recovery, it is 78 possible to use numerical experiments to understand relationships between time since burning, the spatiotemporal patterns of 79 rainfall over a watershed, and the occurrence of flash floods.

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Here, we use realistic patterns of spatially and temporally varying radar-derived rainfall over a 41.5 km 2

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We sought to identify storms in the study area that produced moderate-to-high intensity rainfall to use as inputs to a hydrologic 126 model to simulate flood responses. Storm events were selected within the period for which observations are archived for the two operational NWS Next-Generation Weather Radar installations (NEXRAD; NOAA 1991) that cover the study area, 128 KSOX, (Santa Ana), and KVTX (Ventura). Though archives for the radars begin in 1997 and 1995, respectively.

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We compiled storm events starting with those known to have produced high intensity rainfall and a debris flow response in 131 the San Gabriel Mountains (e.g., Table 1

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We used 15 mm/h as a threshold for moderate to high intensity rainfall and extracted all events from the gauge record meeting 137 or exceeding this value to develop a list of events of interest. We reviewed the radar data for these events at which point some 138 of the selected events could not be utilized due to radar outages or poor data quality. This exercise presented us with 34 storm 139 events (Table S1).

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Various atmospheric processes may contribute to generation of moderate-to-high rainfall intensities (e.g., Oakley et al. 2017), 142 resulting in differing spatial and temporal precipitation patterns over a burn area. To ensure the events selected captured 143 variability in spatial and temporal precipitation characteristics, we evaluated the spatial characteristics of the events. We found 144 rainfall patterns could generally be categorized into four main spatial patterns at the scale of several tens of kilometers: (1) a 145 broad pattern, a contiguous area of moderate-to-high intensity precipitation (>45 dBZ) spanning tens of kilometers; (2) a 146 scattered pattern with numerous cells of moderate to high precipitation that are not spatially continuous; (3) an isolated pattern, 147 with one to a few isolated cells of moderate-to-high intensity rainfall separated by non-precipitating areas several to tens of 148 kilometers in extent; (4) a narrow cold frontal rainband (NCFR)-a north-south oriented narrow band (~3-5 km wide, tens to  Level-II base reflectivity (https://www.ncdc.noaa.gov/wct/) between the start and end time of each event was downloaded 160 from both the KSOX and KVTX radars. The data were used to generate spatially-distributed precipitation over the study area.

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Radar imagery concurrent with the gauge-based record of high intensity rainfall events was converted to a composite maximum 162 reflectivity product at 250 m spatial and 5-minute temporal resolution. Conversion of radar reflectivity to rain rate required 163 the application of an empirically derived reflectivity (Z) to rain rate (R) relationship (e.g. Marshall and Palmer 1948).

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It is worth noting that a number of additional sources of radar measurement uncertainty exist that are not evaluated in depth 172 here, including beam broadening, topographic blocking and scan elevation. However, this was not of primary concern since 173 the goal of this study was to generate realistic spatial and temporal patterns of rainfall over the watershed with varying intensity 174 that could be used to force the KINEROS2 hydrologic model. The goal was not to reproduce the observed hydrologic response 175 resulting from a particular set of rainstorms.

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As a range of precipitation intensities for each storm result from the application of the five different Z-R relationships (e.g., 178 Figure S2 in Supplement), we utilize these as realistic storms of varying precipitation intensity to increase our storm sample 179 size, such that we apply 34 storms * 5 Z-R relations = 170 precipitation scenarios as inputs to KINEROS2. These 170 scenarios 180 were then processed for ingestion into KINEROS2 ( Figure. 2).

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In search of a spatiotemporel summary metric that may serve as a reliable flash flood threshold, we begin by describing a 187 methodology to summarize spatially and temporally varying rainfall over a watershed. For a given rainstorm, the rainfall 188 intensity time series at a single point, such as a single radar pixel, can be summarized by computing a moving average of 189 intensity over a specified duration, D. Letting t denote time and R denote the cumulative rainfall (mm), we define the rainfall 190 intensity over a duration D at any given pixel within the watershed as Here, we compute ሺ ሻ for each pixel for durations of 5, 10, 15, 30, and 60 minutes. Since the intensity in each radar pixel 193 could have a unique value, we also need a way to summarize ሺ ሻ in space. One option would be to take the median of ሺ ሻ

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The first approach is based on a linear regression analysis that relates peak discharge with different rainfall ID metrics, namely

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The rainfall intensity thresholds at each percentile significantly increased from post-fire year 1 to 5 (Figures 4 and 7). However, 330 the increase from year 1 to 2 is considerably larger than that from year 2 to 3 or from year 3 to year 5. Taking the 30 75 (the 75 th 331 percentile of the peak I 30 rainfall field) as an example due to its strong performance as a threshold for all post-fire years, the

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We are also able to use the model to assess the individual impacts of temporal changes in K sh and n c on temporal variations in 336 the flash flood threshold. If K sh is allowed to vary from year to year (Table 1) and n c is held fixed at its calibrated value for year 1, then ROC analysis indicates that the optimal threshold of 30 75 still increases with time since burning (Figure 8).
However, it increases slower than the case where both K sh and n c are allowed to vary with time ( Figure 8). If n c is allowed to 339 vary from year to year (Table 1)

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Red contours delineate the pixels with rainfall intensities larger than 30 75 of each storm.

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Several limitations are present in this work. First, we assess a small number of storm events (34) in the area as we are limited 392 by the length of radar and gage records as well as and the number of events that impact the indicator rain gages. However, the 393 advantage of using observed storms rather than using a rainfall generator (e.g.