Parsing Weather Variability and Wildfire Effects on the Post-Fire Changes in Daily Stream Flows : A Quantile-Based Statistical Approach and its Application

Abstract

Determining wildland fire impacts on streamflow can be problematic as the hydrology in burned watersheds is influenced by post-fire weather conditions. This study presents a quantile-based analytical framework for assessing fire impacts on low and peak daily flow magnitudes, while accounting for post-fire weather influences. This framework entails (a) the bootstrap method to compute the relative change in the post-fire annual flow and weather statistics, (b) Double Mass analysis to detect if post-fire baseflow and quick flow yield ratios are significantly altered, and (c) a quantile regression method to parse fire effects on flow at a specific quantile. We illustrate the applicability of this analytical framework using 44 western US streams with at least 5% of their watershed area burned. Results indicate that large, high-severity burns in upland watersheds can raise the streamflow magnitude at the 0.05^th and 0.95^th quantiles for at least the five post-fire years. Quantile regression results show that the median fire-related increase in flow for the five post-fire years can be up to 5000% (Standard Error; SE < 2%) at the 0.05^th quantile and 161% (SE < 10%) at the 0.95^th quantile. The fire-related increase in flow was often pronounced at the 0.05^th quantile for streams in the Pacific Northwest and California regions. The difference in fire effects on flow (at both quantiles) across streams was related to post-fire weather, pyrology, physiography, and land cover. The proposed analytical framework can be useful for detecting and quantifying fire effects on the low and peak stream flows in burned watersheds without overlapping disturbances.

1. Introduction

The western United States (WUS) is a water stressed region with a large and growing human population (Pierce et al., 2008). Nearly two-thirds of the freshwater supply in the WUS is derived from streams downgradient of forested watersheds (Furniss, 2010). Water managers in this region are concerned about the potential implications of climate and human-induced forest disturbance on their water resources as forest disturbances can alter the water yield from upland watersheds (Rieman et al., 2005; Barnett et al., 2008; Bladon et al., 2014). However, even in natural watershed settings where anthropogenic influences on the landscape hydrology are minimal, evaluation of the impacts of forest disturbances on downstream hydrology is not straight forward. Prevailing weather conditions can enhance or attenuate forest disturbance effects on streamflow as meteorological variables (e.g., precipitation, evaporation) exert a significant control on the amount of moisture that can be converted into flow (Dooge, 1992; Krakauer & Fung, 2008). Also, likelihoods of forest disturbances such as forest fires and pests are influenced by weather or climate events such as droughts and lightnings (Abatzoglou & Williams, 2016; Brey et al., 2018). Such complexities make the assessment of forest disturbance impacts on streamflow regimes challenging.

Over the last three decades, the frequency of large, high-severity fires has risen across many WUS regions due to the commingling effects of a warming climate, excess forest fuel buildup, and increases in the wildland-urban interface (Dennison et al., 2014; Abatzoglou & Williams, 2016). High severity fires can alter key catchment hydrological processes (e.g., infiltration, evaporation, interception) such that the water yield is substantially enhanced (DeBano, 2000; MacDonald & Huffman, 2004; Kunze & Stednick, 2006). Consequently, intense storm or snow-melt events following extensive, severe burns in upland basins can trigger massive flash floods and sediment and nutrient flow which impair downstream water supplies (Emelko et al., 2011; Bladon et al., 2014), human life and property (Jordan & Covert, 2009), and aquatic ecology (Rieman et al., 2005; Silins et al., 2014). The development of fire adaptation and mitigation strategies for water resources in the WUS hinges upon understanding potential streamflow responses to watershed burn effects. To this end, various topics related to wildland fire impacts on daily-to-annual streamflow have been studied (Moody et al., 2013, and references therein). However, two critical features on the nature of post-fire changes in the streamflow regime have received less attention. One is the asymmetry in the yearly low and peak streamflow response to fire effects. Another is the spatial diversity in the fire-related changes in the annual peak and low flows.

Only a few studies have examined the nature and extent of the fire-related annual peak flow and/or low flow changes in burned WUS watersheds. In these studies, fire corresponded to an increase in annual low and peak flows by up to 1090% (Seibert et al., 2010; Chen et al., 2013; Wagenbrenner, 2013; Kinoshita & Hogue, 2015). Moreover, the association between watershed burning and higher peak flows was related to changes in critical hydrologic processes and components such as lower plant transpiration and interception rates, enhanced snow accumulation, and reduced infiltration rates leading to higher infiltration excess overland flow (Seibert et al., 2010; Wine & Cadol, 2016; Chen et al., 2013). Similarly, studies linked the enhancing effect of fire of low flows to lower plant transpiration, deeper infiltration and enhanced preferential subsurface flows, earlier soil thawing and prolonged soil drainage period, and a subsequent rise in subsurface storages and baseflow (Ebel et al., 2012; Stoof et al., 2014; Cardenas & Kanarek, 2014; Kinoshita & Hogue, 2015; Bart & Tague, 2017). On the other hand, there is evidence that fire-induced changes in the yearly low and peak streamflow may not be the same. Kinoshita and Hogue (2015) found that the post-fire low flows were, on average, 1090% and 118% higher than that of the pre-fire in two Californian watersheds with extensive burns. However, they detected negligible changes in the two watersheds’ post-fire annual peak flows. Alternatively, Wine and Cadol (2016) discerned a significant fire-induced increase in the annual peak flow but not in the annual low flow in two New Mexico watersheds that burned. Conducting an analysis of the fire-related annual peak and low flow changes across multiple burned watersheds offers the opportunity to detect and understand the symmetry/asymmetry in post-fire daily flow alteration in the WUS.

In natural watershed settings, empirical wildfire studies often favor using a paired watershed (burned and unburned) comparison approach, often in a before-after-control-impact design, to assess wildfire impacts on low and peak flows low (e.g., Moody & Martin, 2001; Owens et al., 2013). This is because the approach allows estimation of the fire related change in low/peak flows simply as the deviation from the pre-fire flow correspondence between the paired watersheds. Nevertheless, given that not many watersheds have pre-fire flow data, the paired watershed comparison approach may not be applicable in most burned sites to disentangle the effects of wildfire from other factors (e.g., geography, weather) that can lead to context dependency in low/peak flow responses. Moreover, conditions (e.g., weather, landcover) even among contiguous catchments may not be analogous especially in mountainous settings (Hallema et al., 2017). These limit the application of paired watershed comparison approach in conducting local and regional wildfire-stream flow studies in the western US.

Recent empirical studies have demonstrated that time trend analysis, sensitivity-based methods, and other statistical approaches that utilize streamflow data only from burned watersheds can be effective in detecting and quantifying forest disturbance impact on annual streamflow (e.g., Zhao et al., 2010; Biederman et al., 2015; Wine & Cadol, 2016; Hallema et al., 2017; Saxe et al., 2018). In these approaches, the pre-disturbance relations between annual meteorological (e.g., precipitation, evaporation) conditions and streamflow serve as the basis for characterizing disturbance effects on the post-fire annual streamflow. The application of these statistical approaches in evaluating forest disturbance impacts on low and peak flows is, however, limited as many (e.g., Double Mass Analysis, Trend Analysis) would require arbitrary subsampling of streamflow data and distributional assumptions. In contrast, the quantile regression approach(Koenker & Bassett, 1978) can be used to develop quantile specific relations between weather variables and daily flow without the need for (a) any distributional assumptions, (b) subsampling of flow data, and (c) removing outliers. This study will demonstrate how quantile regression models can be used in approximating fire related flows in the WUS.

This study aims to propose a novel quantile-based analytical framework that can be used to infer wildfire impacts on the annual low and peak flows in streams while accounting for post-fire weather effects. We refer to post-fire weather (or weather variability) effects as those directly arising from the difference in the pre-and post-fire weather conditions. Unlike the paired watershed method, this framework requires pre-and post-fire streamflow data for the burned watershed site only. Moreover, the framework encompasses a suite of empirical methods (namely bootstrap method, double mass analysis and quantile regression approach) that in combination can be used to infer the response of annual low and peak flows to fire effects.

2. Data Sources and Methods

The objective of this study is to describe and demonstrate a quantile-based analytical framework for assessing wildfire impacts on annual low and peak flows. The next section describes stream site selection criteria and the national datasets accessed to derive the pyrologic, hydrologic, climatic, and topographic data for their watershed (Section 2.1). Section 2.2 discusses the three empirical methods encompassed in the proposed analytical framework to evaluate wildfire’s influence on the yearly low and peak stream flows. Figure 1 depicts the analytical framework adopted in this study.

Figure 1:

Quantile-based procedural framework for assessing fire impacts on annual and seasonal low and peak flows

2.1. Watershed Selection and Data Sources

For selecting stream sites with burned watersheds for this study, we first obtained geospatial wildfire data for the United States from the Monitoring Trends for Burn Severity (MTBS; Eidenshink et al., 2007) project database. MTBS project databases currently have the most extensive compilation of burn extent and severity records for wildland fires of size greater than 4 km² in the WUS from 1984 – 2018. Next, burn perimeters of wildfires were cross-referenced with the watershed delineations of reference US Geological Survey (USGS) Geospatial Attributes of Gages for Evaluating Streamflow version 2 (GAGES II; Falcone, 2011) stream sites to determine reference GAGES II stream sites with burned watersheds. We then considered all reference GAGES II stream sites with burned watersheds for inclusion based upon meeting the following three criteria. First, streams were required to have a wildfire burn event(s) within a single year between 1988–2013 in their watershed, where (a) at least 5% of the watershed area was burned and (b) no other fire(s) had burned more than 3% of their watershed area in the preceding and following 5–15 years. Second, streams needed to have at least ten years of uninterrupted and contiguous streamflow data: 5–13 years of pre-fire data and five years of post-fire data. A longer pre-fire period data (> 5 years) was sought because this is used as the base period up on which we can assess wildfire effect on low and peak streamflow. The final criterion required that WUS streams with zero flow days be excluded as we wanted our definition of the annual period to be consistent across studied streams. A total of 44 stream sites met these criteria and thus were retained in this study for subsequent analysis Figure 2a.

Figure 2:

Location map of selected streams and summaries of their watershed’s burn (burn area, timing), topographic (area, slope), climatic (annual precipitation, temperature), and hydrologic (baseflow index) characteristics.

We accessed several national datasets to derive the pyrologic, hydrologic, climatic, and topographic data for the watersheds of the 44 selected stream sites (Table S1). Spatial attributes of the wildfire burn area and severity for these watersheds were obtained from MTBS project burn severity rasters. The National Hydrography Dataset Plus-version 2 (NHD Plus V2; McKay et al., 2012) datasets were also acquired to compute the physiographic (Elevation, Slope) data for the burned watersheds (Supplementary S1). In addition, watershed averaged daily air temperatures and precipitation totals from 1979–2018 were estimated from gridded Parameter-elevation Regressions on Independent Slopes Model (PRISM; Daly et al., 2002) datasets. Monthly accumulated potential evapotranspiration (PET) totals were obtained from the University of Idaho’s Gridded Surface Meteorological Dataset (GRIDMET; Abatzoglou, 2013) dataset. Land cover types and soil types and properties at each watershed were derived from the 2001 National Land Cover dataset (NLCD2001; Homer et al., 2004) and US Department of Agriculture’s Digital General Soil Map of the United States (STATSGO; Schwarz & Alexander, 1995) datasets respectively. The watershed’s compound topographic index (CTI; Moore et al., 1991) was obtained from USGS’s HYDRO1k Elevation derivative database. Finally, the boundaries for US water resource regions (WRR; Seaber et al., 1987) —which represent either the drainage boundaries of a major river or the combined drainage areas of a series of rivers with similar hydrologic characteristics — were collected from USGS’s WBD (Watershed Boundary Dataset;https://water.usgs.gov/GIS/huc.html). Figures 2a–e depict the distribution of selected streams in the WUS and summarizes their watershed burn (burn area, timing), topographic (area, slope), climatic (annual precipitation, temperature), and flow (baseflow index) attributes. Tables 1 and S2 also include additional attributes.

Table 1.

Watershed physiography and pyrology of studied streams.

USGS Gage Stations	State	Study Years	Mean Basin Slope (%)	Watershed Area (km2)	Mean Basin Elevation (m)	Water Resources Regions	%Watershed Area Burned (Year)	Watershed area burned under high severity (%)	Nearest distance from Burned Area (km)
06036905	Montana	1983–1993	9.9	677	2429	Missouri	52.4 (1988)	31	0
06137400	Montana	1983–1993	30.5	63.5	1455	Missouri	25.6 (1988)	8.4	1.6
06154410	Montana	1982–1993	32	33	1386	Missouri	21.5 (1988)	12.1	3.5
06191500	Montana	1980–1993	24.7	6783	2543	Missouri	44.8 (1988)	19.8	12.7
06224000	Wyoming	2000–2017	31.7	485	3139.4	Missouri	21.6 (2012)	6.6	4.4
06280300	Wyoming	2004–2018	44.7	794	2819.4	Missouri	13.4 (2013)	7.5	22.6
08324000	New Mexico	1997–2016	23	1207	2612	Rio Grande	8.7 (2011)	4	16.7
08377900	New Mexico	1997–2006	28	139	3170	Rio Grande	9.4 (2002)	3.1	9.8
08378500	New Mexico	2000–2018	31	445	3078	Rio Grande	9.6 (2013)	5.4	0.09
08386505	New Mexico	2001–2017	40	49	2847	Rio Grande	10 (2012)	4.1	6.2
09210500	Wyoming	1989–2005	19.8	398	2487	Upper Colorado	14.2 (2000)	4.5	14.9
09223000	Wyoming	2000–2015	20.4	333	2581	Upper Colorado	5.2 (2001)	1.4	0.3
09404450	Utah	2000–2017	31.3	193	2225	Great Basin	14.3 (2012)	7.6	9.4
09494000	Arizona	1992–2008	20.7	1628	2255	Lower Colorado	5.1 (2003)	3.7	13.1
09497800	Arizona	1989–2007	27.8	751	1750	Lower Colorado	33.6 (2002)	23.6	27.1
09497980	Arizona	1996–2017	28.9	517	1706	Lower Colorado	7.9 (2012)	1.8	36.9
09505200	Arizona	1997–2014	14.1	286	1954	Lower Colorado	5.3 (2009)	0.8	16.5
10172700	Utah	1980–1995	21.2	70	2164	Great Basin	26.6 (1990)	8.7	2.3
10329500	Nevada	1996–2012	21	455	1893	Pacific Northwest	7.2 (2007)	2.6	0.3
10396000	Oregon	1987–2004	16.2	528	1889	Pacific Northwest	5 (1999)	1.1	17.7
11098000	California	Discharge	57.2	41	1097	California	100 (2009)	77.5	0
11383500	California	1982–1995	28.2	540	1280	California	21.3 (1990)	6.9	0
11427700	California	1988–2006	30.6	25	1950	California	39.7 (2001)	16.5	0
11451100	California	1986–2001	38.9	155	911	California	99.4 (1996)	76	0
11473900	California	1980–2013	32.4	1925	1123	California	10.5 (2008)	2.2	11.2
12358500	Montana	1991–2008	45.5	2939	1721	Pacific Northwest	10.4 (2003)	5.2	0.3
12374250	Montana	1995–2012	28.7	50	1414	Pacific Northwest	99.8 (2007)	65.3	0
12447390	Washington	1991–2008	41	58	1939	Pacific Northwest	96.3 (2003)	66.6	0
12448000	Washington	1991–2008	36.3	1357	1612	Pacific Northwest	22.6 (2003)	15.9	24.2
12448500	Washington	1991–2008	43.7	2683	1591	Pacific Northwest	14.4 (2003)	9.7	24.5
12452800	Washington	1988–1999	48.9	526	1520	Pacific Northwest	10.9 (1994)	5.5	0
13011900	Wyoming	1998–2017	27	852	2728	Pacific Northwest	16.2 (2012)	9.2	20.7
13161500	Nevada	1984–1997	25	986	2045	Pacific Northwest	14.8 (1992)	0.6	0.5
13185000	Idaho	1984–1999	44.3	2154	1954	Pacific Northwest	27.7 (1994)	11.1	1
13237920	Idaho	2000–2011	42	874	1661	Pacific Northwest	16.6 (2006)	6.8	11.4
13240000	Idaho	1984–1999	42.1	125	2109	Pacific Northwest	16.7 (1994)	7	2.7
13296500	Idaho	2001–2017	33.6	2375	2091	Pacific Northwest	15.4 (2012)	7.5	0.6
13310199	Idaho	1994–2004	45.4	7451	2161	Pacific Northwest	17.6 (1999)	8.1	5
14092750	Oregon	2000–2017	14.8	57	1479	Pacific Northwest	76.2 (2012)	47	1.3
14096300	Oregon	1988–2006	20.7	68	1455	Pacific Northwest	12.4 (2001)	6.9	10.4
14096850	Oregon	1984–2001	12.7	375	943	Pacific Northwest	12.1 (1996)	2.7	3.6
14158500	Oregon	1991–2008	18.5	237	1253	Pacific Northwest	8.6 (2003)	3.6	9.1
14400000	Oregon	1991–2007	42.5	702	671	Pacific Northwest	74.7 (2002)	38.2	11.1
402114105350101	Colorado	2002–2017	45	105	3235	Pacific Northwest	10.1 (2012)	5.3	4.2

2.2. Detecting and Estimating Wildfire Impact on the Magnitude of Lower and Upper Streamflow Quantiles

Quantiles (τ) are locations in the cumulative distribution function which correspond to the rank order of values in the distribution. For example, for any daily streamflow distribution, 95% of the daily flows have values greater than the 0.05^th flow quantile. In this study, we selected daily flows at the lowest and highest 0.05^th quantiles in any year to represent annual low and peak flow events.

The proposed quantile-based framework includes three empirical methods:

• Bootstrap method to determine the post-fire change in annual weather (here precipitation) and flow statistics

• Double mass analysis of cumulative annual flow components (baseflow and quick-flow) and precipitation totals.

• Quantile regression method to parse and estimate wildfire and weather contributions on the post-fire changes in low and peak flow magnitudes.

The hydrology in the selected stream sites is considered to be minimally impacted by direct human activities. Hence, all three empirical methods assume that pre-fire streamflow and weather conditions in selected streams as reference conditions up on which wildfire impacts on natural flow can be determined. On the other hand, the framework utilizes multiple empirical methods for two reasons. One is because they address various aspects of the post-fire change in annual low and peak flows. Another is because of the limited number of pre-fire flow data available in the selected watersheds (5–15 years), it is very hard to compare across analytical methods. Hence it makes sense to utilize multiple methods and observe the consistency across results.

2.2.1. Bootstrap approach

The bootstrap method (Efron, 1982) was used to compare pre-and post-fire annual precipitation and flow statistic in studied stream sites. In the bootstrap method, we randomly shuffled (with replacement) the pre-fire years to generate 1000 subsamples of size equal to the post-fire year length (n = 5). For stream sites with matching fire year, the shuffling of the pre-fire years was conducted in the same way to preserve the spatial coherence between sites (Livezey & Chen, 1983). For each subsample, the median of the flow and precipitation statistics was determined. The change in annual precipitation or flow statistics following a wildfire was computed as the difference between the median of the post-fire precipitation or flow statistics and the 500^th ranked subsample value. The post-fire precipitation or flow statistics was also assumed to be significantly changed if the median of the post-fire annual precipitation or flow statistics was outside of the 50^th to 950^th ranked sub-sample values (Figure 3a).

Figure 3:

Illustrations of how the three analytical approaches included in the proposed framework work using observed data: (a) Bootstrap method, (b) Double mass regression analysis, and (c) Quantile regression approach. In the quantile regression approach, $\Delta Q_{\mathit{\text{Tot}}}^{\left(0.95\right)}$, $\Delta Q_{\mathit{\text{Weather}}}^{\left(0.95\right)}$, and $\Delta Q_{\mathit{\text{Fire}}}^{\left(0.95\right)}$ represent the post-fire change, weather-related change, and fire-related change in the magnitude of streamflow at the 0.95^th quantile, respectively. ${\tilde{Q}}_{\mathit{\text{prefire}}}^{0.95}$ denotes the median magnitude of pre-fire flow at the 0.95^th quantile

2.2.2. Double mass analysis

Changes in annual baseflow and quick-flow amounts are typically related to annual low and peak flow variability in streams (Buttle, 2018; Ficklin et al., 2016). In the double mass analysis, we compared regression lines for the pre-and post-fire cumulative annual precipitation-baseflow and annual precipitation-quick flow data to determine if the burning of watersheds significantly altered the annual baseflow and quick-flow yield ratios in studied streams (Figure 3b). This method has been proven to be an effective way of detecting the post-fire change in the annual streamflow yield ratio (Wei & Zhang, 2010).

First, the Lyne-Holick recursive digital filtering method (Lyne & Hollick, 1979) was applied to split the annual streamflow hydrograph into baseflow (slowly varying flow component) and quick-flow (rapidly varying flow component). Two dynamic regression models (Pankratz, 2012) for the cumulative annual precipitation-baseflow data were fitted for the pre-and post-fire years separately (restricted) and collectively (unrestricted). Similar regression models were also developed for the cumulative annual precipitation-quick-flow data. The general form of these double mass (DM) regression models is

$$Q={\beta }_0+{\beta }_1*(1-X)+{\beta }_2*(1-X)*(1-PPT)+{\beta }_3*(X)*(PPT)+ϵ$$ (1)

where β represent parameter estimates (coefficients), and PPT and Q denote cumulative annual precipitation and annual baseflow (or quick-flow) variables, respectively. X is a time parameter which equals one in the unrestricted model. In the restricted DM regression model, X equals zero and one respectively if the observation year precedes and follows the fire year. ϵ was the residual term of the regression that is modeled by the Auto-Regressive Integrated Moving Average model (ARIMA; Box & Jenkins, 1976).The ARIMA model function is represented by (p, d, q) with p representing the number of autoregressive terms, d the number of non-seasonal differences needed for non-stationarity, and q the number of preceding/lagged forecast errors in the prediction equation. The forecast package (Hyndman et al., 2020) in the R computing environment provides the optimizing algorithm to estimate the coefficients in these DM regression models.

Likelihood Ratio Test (LRT; Snedecor & Cochran, 1989) was then used to compare the relative goodness of fit of the restricted and unrestricted DM regression models. In this test, the null hypothesis is that the variability in the post-fire yearly quick-flow or baseflow yield ratios is the same as that of the pre-fire and thus the restricted DM regression model does not offer an appreciable improvement over the unrestricted regression model in representing the annual baseflow or quick-flow yield ratio variability over the pre- and post-fire periods. Alternatively, if the LRT statistic falls below 0.10, this study assumed that the restricted DM regression model is superior to the unrestricted DM regression model in characterizing the variability in the pre- and post-fire annual quick-flow or baseflow yield ratios. This, in turn, implies a change in the cumulative yearly precipitation-baseflow or quick-flow relationship following the fire and that the fire year represents the breaking point in that relationship.

2.2.3. Quantile regression approach

The quantile regression approach was used to parse and quantify weather and fire effects on daily streamflow at the 0.05^th and 0.95^th quantiles. This approach involved three steps. Multiple sets of candidate Linear Quantile Regression models (LQR; Koenker & Bassett, 1978) for daily streamflow at the 0.05^th and 0.95^th quantiles under baseline (undisturbed) conditions were first constructed and fitted using pre-fire weather and streamflow data. Next, best fit model for flow at each quantile were selected based on their relative fitness. The predictive performances of selected models for flows at the two quantiles under undisturbed conditions were evaluated using the Leave One Out Cross Validation (LOOCV) method. Finally, the post-fire annual weather statistics was input into the best fit LQR models to estimate the daily streamflow at the 0.05^th and 0.95^th quantiles for each post-fire year assuming no fire disturbance. Fire-related change in the magnitude of flow at a selected quantile for the five post-fire years was then computed as the median difference between observed and model estimated post-fire stream flow magnitudes at the selected quantile (Figure 3c).

During LQR model building, twenty seasonal-to-annual weather variables (related to precipitation, potential evapotranspiration, and air temperature) were considered as possible covariates (see Table 2), and thus multiple sets of candidate LQR models for daily streamflow at each quantile were fitted. Generally, these candidate models have the functional form

$$Q^{(\tau )}={\beta }_0^{(\tau )}+{\beta }_1^{(\tau )}{X}_1+{\beta }_2^{(\tau )}{X}_2+{ϵ}^{(\tau )}$$ (2)

where Q^(τ) and β^(τ) represent the daily streamflow and parameter estimates for weather covariates at the τ^th quantile, respectively. X₁ and X₂ denote the seasonal-to-annual weather covariates and ϵ^(τ) signifies the error term with an unknown distribution at the τ^th quantile (0.05^th and 0.95^th). The maximum number of covariates included in these models was set at two to avoid overfitting the models. The Pearson’s correlation between any two covariates in a candidate model was also set not to exceed 0.70 to preclude potential multicollinearity issues. Finally, a potential problem with developing LQR models for daily streamflow at the 0.05^th and 0.95^th quantiles is that the autocorrelation in the daily streamflow time series is likely to inflate the relative importance of covariates included in LQR models. Thus, the statistical significance of parameter estimates (β^(τ)) in candidate LQR models was tested using the approach proposed by Franzke (2013). The quantile regression implementation in the R computing environment (Koenker, 2017) provided the optimizing algorithm to estimate β^(τ) for these covariates at the 0.05^th and 0.95^th quantiles.

Table 2:

List of seasonal-to annual-weather covariates considered in our quantile regression models for streamflow at the 0.05^th and 0.95^th quantiles. PET is an abbreviation for Potential Evapotranspiration.

Fall precipitation totals	Winter precipitation totals	October-March precipitation totals
Spring precipitation totals	Summer precipitation totals	Annual precipitation totals
Fall PET Totals	Winter PET totals	Spring PET totals
Summer PET totals	Annual PET totals	Average fall air temperatures
Average Winter Air Temperatures	Average Spring Air Temperatures	Average summer air temperatures
Average annual air temperatures	Antecedent summer precipitation totals	Previous year’s annual precipitation totals
Antecedent summer PET totals	Previous year’s annual PET totals

During model selection, we used the bias-corrected Akaike Information Criterion (AICc; Akaike, 1974) to compare the complexity and goodness of fit of candidate LQR models at the 0.05^th and 0.95^th quantiles. Best fit LQR models at both quantiles were selected as those with the least AICc score. The predictive performance of the best fit LQR models under undisturbed conditions was then assessed using the LOOCV approach. This involved withholding the weather and streamflow data for each pre-fire year, re-calibrating the LQR model parameters to the remaining data, and making daily streamflow predictions at the 0.05^th and 0.95^th quantiles for the left-out year, and then repeating the procedure for all pre-fire years. We compared LOOCV predicted daily streamflow values with that of the observed using three model performance metrics: Nash-Sutcliffe coefficient of model efficiency (NSC; Nash & Sutcliffe, 1970), percent bias (%bias), and relative root mean squared error (rRMSE)- the root mean squared error normalized by the observed mean. NSE measures the total model residual flow error relative to the total variance within the flow data. Percent bias estimates the tendency of a selected model to over predict (%bias < 0) and underpredict (%bias > 0) streamflow under undisturbed conditions. Note that if a model overpredicts streamflow by 1% under undisturbed conditions, it means that the model is likely to underpredict fire effects on streamflow by the same amount. rRMSE measures the absolute error in model flow estimates relative to the observed mean flow value.

Given that multiple sites were evaluated in this study, the results from this quantile regression approach can be leveraged to offer some insights into the watershed attributes that mediate wildfire effect on post-fire annual flows at the 0.05^th and 0.95^th quantiles. Hence, we used random forest models (Breiman, 2001) to regress the the median fire-related change in flow ($\Delta Q_{\mathit{\text{fire}}}^{(\tau )}$) at the 0.05^th and 0.95^th quantiles across all sites against a subset of 36 watershed variables (see Table 3). Random forest is a machine learning algorithm capable of handling large nonlinear, noisy, fragmented, or correlated multidimensional data for classification or regression. A random forest regression model is built by constructing ensembles of regression trees trained using recursive subsets of all observations, and predictions are computed as the expected value of all individual predictions from each tree in the random forest model (Cutler et al., 2007). We developed the two random forest models by iteratively inputting predictor(s) that produced the greatest improvement in the models’ mean squared errors and were physically interpretable. We stopped the selection processes when the addition of any predictor did not reduce the mean squared error by 0.10. Moreover, the importance of a predictor variable in a model is estimated by computing the mean decrease in accuracy (Mean Squared Error) observed between model predictions and actual values by randomly permuting a selected variable (Breiman, 2001). We used the randomforest package (Liaw et al., 2002) in the R computing environment to build random forest regression models for $\Delta Q_{\mathit{\text{fire}}}^{(\tau )}$ values at the 0.05^th and 0.95^th quantiles.

Table 3:

List of watershed attributes considered in the random forest regression models for fire effects on the 0.05^th and 0.95^th quantile flows.

Latitude	Longitude	Burned watershed area (%)
Watershed area burned under high severity (%)	Burned riparian area (%)	Riparian area burned under high severity (%)
Station’s nearest distance from the burn area (m)	Watershed Area (km2)	Mean watershed elevation (m)
North facing watershed area (%)	South facing watershed area (%)	Mean watershed slope (%)
Annual PET totals (mm)	October-March precipitation totals (mm)	Annual precipitation totals (mm)
Mean annual air temperature (C)	Summer PET totals (mm)	Mean fall air temperature (C)
% change in summer PET total	% change in fall PET totals	% change in October-March precipitation totals
% change in annual precipitation totals	% change in spring precipitation totals	% change in summer precipitation totals
Forested watershed area (%)	Barren watershed area (%)	Shrubbed watershed area (%)
Open water watershed area (%)	Grassland watershed area (%)	Fall baseflow index (%)
Soil permeability (in/hr)	Summer baseflow index (%)	Annual baseflow index (%)
Compound topographic index	Winter baseflow index (%)	Spring baseflow index (%)

3. Results

3.1. Streamflow and Weather Comparison

Post-fire stream flows at the 0.05^th and 0.95^th quantiles were generally higher than to that of the pre-fire period for 29 and 21 stream sites, respectively (Figure 4a and b). Across these streams, the median increase (percent- %) in the magnitude of flow for the five post-fire years ranged from 1–5300% at the 0.05^th quantile and 1–166% at the 0.95^th quantile, relative to that of the pre-fire. The post-fire increase in flow at the 0.05^th and 0.95^th quantiles was statistically significant (p < 0.10) for 19 and 9 of these streams, respectively (Figure 4a and b). A significant post-fire increase in flow magnitude at both 0.05^th and 0.95^th quantiles was observed for only seven stream sites. In contrast, post-fire stream flows at the 0.05^th and 0.95^th quantile were generally lower than that of the pre-fire for 14 and 23 stream sites, respectively (Figures 4a and b). Across these streams, the median decrease in the magnitude of flow at the 0.05^th and 0.95^th quantiles for the five post-fire years ranged from 1–66%, relative to that of the pre-fire. The post-fire decrease in flow at the 0.05^th and 0.95^th quantiles was statistically significant (p < 0.10) for five and three stream sites. A significant post-fire decrease in flow at both 0.05^th and 0.95^th quantiles was found at only one stream site. Streams where the post-fire change in flow at 0.05^th and 0.95^th quantiles were significant at p < 0.05 are shown in Figure S1.

Figure 4:

Post-fire change (%) in the magnitude of daily flow at the 0.05^th and 0.95^th quantiles across the studied stream sites, and its correspondence to watershed area burned and post-fire annual precipitation change. (a-b) Post-fire change burned in daily stream flow magnitudes at the 0.05^th and 0.95^th quantiles across the studied streams. (c) Post-fire change (%) in the watershed averaged annual precipitation total across the studied streams. Filled triangles represent stream sites where the change in annual precipitation and flow statistics was significant at p < 0.10. (d-e) The direction of post-fire flow change at the 0.05^th and 0.95^th quantiles associated with the watershed area burned and post-fire annual precipitation changes.

Prior to the fire disturbances, the watershed averaged annual precipitation totals across studied streams were positively correlated to the flows at the 0.05^th (average Pearson’s correlation coefficient r = 0.60) and 0.95^th (average Pearson’s correlation coefficient r = 0.87) quantiles. Although the post-fire watershed averaged annual precipitation in over 85% of the studied stream sites was not significantly different from that of the pre-fire period, the median change in the annual precipitation totals for the five post-fire years across stream sites ranged from −40% – +60% relative to that of the pre-fire (Figure 4c). The greatest post-fire increase in the watershed averaged annual precipitation were recorded in sites in the eastern part of the Pacific Northwest (PNW) region. Across the studied streams, the direction of change in annual precipitation generally corresponded to the direction of post-fire change in flow at both 0.05^th and 0.95^th quantiles (Figures 4d and e). Nevertheless, decreases in post-fire annual precipitation were accompanied by increases in flow at the 0.05^th quantile and to a lesser extent flow at the 0.95^th quantile for the same period for about half a dozen stream sites with a burned watershed area greater than 13% (Figures 4d and e).

3.2. Double mass analysis

Pre-fire daily flow magnitudes at the 0.05^th quantile across the studied stream sites were strongly related to the annual baseflow (average Pearson’s correlation coefficient r = 0.77) and quick-flow (average Pearson’s correlation coefficient r = 0.70) totals. Similarly, Pearson’s correlations between the 0.95^th quantile daily flow magnitudes and the yearly baseflow and quick flow totals at the studied streams were 0.93 and 0.98, respectively. A log-likelihood ratio-based comparison of the unrestricted and restricted DM regression lines for cumulative annual precipitation-baseflow and cumulative annual precipitation-quick-flow totals in the studied streams indicates significant (p <0.10) alterations in the post-fire annual baseflow and quick-flow yield ratio in 19 and 14 studied stream sites, respectively (Figure 5a). Significant post-fire changes in the annual baseflow yield ratio and quick-flow yield ratio were often detected in the studied stream sites with a burned watershed area exceeding 25% and to a lesser extent in the stream sites with a burned watershed area between 10–25% (Figure 5b). Alternatively, a significant post-fire change in annual baseflow was found in only one out of the ten studied stream sites with a burned watershed area between 5–10%. Tables S3 and S4 lists the restricted and unrestricted DM models’ coefficients and fitness constructed for the studied streams in this study. Streams where the post-fire change in annual baseflow and quickflow yield ratios were significant at p < 0.05 are shown in Figure S3.

Figure 5:

Typologies of post-fire change in annual quick-flow and baseflow yield ratios across studied streams, and their associations with the burned watershed area. (a) Typologies of post-fire change in annual baseflow and quick-flow yield ratios across studied watersheds. Filled circles denote streams where there was a significant (p <0.10) change in their annual quick flow yield ratio (blue) or baseflow yield ratio (red) or both (magenta). (b) Typologies of post-fire change in annual baseflow and quickflow yield ratios associated with different burned watershed area ranges.

3.3. Quantile regression approach

The best fit LQR models described the flow variability at the two quantiles well and accounted for 80–100% of the total flow variability under undisturbed conditions (Tables S5 & S6). Tables S5 & S6 show the covariates included in these models for studied streams. Model skills during LOOCV evaluations suggest that under undisturbed conditions, the best fit LQR models for the 0.05^th and 0.95^th quantile daily flows were characterized by low rRMSE (< 10%) and %bias (< 5%), and high NSC (> 65%) for the majority of studied stream sites (Figures 6a–f).

Figure 6:

Predictive performances of best fit quantile regression models for streamflow at the 0.05^th and 0.95^th quantiles during a leave one out cross validation: (a and d) relative root mean squared error (%), (b and e) Nash-Sutcliffe coefficient, and (c and f) percent bias.

For each stream site, we used the best fit LQR models to parse weather and fire effects on the daily flow at the 0.05^th and 0.95^th quantiles. Post-fire weather conditions were attributed with at least a 10% (Standard Error; S.E. < 2%) increase and decrease in the magnitude of flow at the 0.05^th quantile at 8 and 13 stream sites, respectively (Figure 7a). Across these streams, the median weather-related change in flow at the 0.05^th quantile for the five post-fire years ranged from 10–238% (S.E. < 2%). High weather-related changes in flow at the 0.05^th quantile were found at stream sites in the California region. Similarly, post-fire weather effects were associated with at least a 10% increase and decrease in the 0.95^th flow magnitude at 19 and 15 streams, respectively (Figure 7b). Across these streams, the median weather-related change in the 0.95^th quantile flow magnitudes for the five post-fire years ranged from 10–195% (S.E. < 10%).

Figure 7:

Fire-and weather-related changes (%) in daily flow at the (a and c) 0.05^th and (b and d) 0.95^th quantiles across studied streams.

Wildfire effects on the flow across studied streams varied depending on the flow quantile and stream site (Figures 7c and d). The burning of watersheds corresponded to at least a 10% (S.E. < 2%) increase in the magnitude of flow at the 0.05^th quantile at 26 stream sites (Figure 7c). Across these streams, the median fire-related increase in flow at the 0.05^th quantile for the five post-fire years ranged from 10–5000% (S.E. < 2%). Strong fire-related increase in flow at the 0.05^th quantile were often detected at stream sites in the Pacific Northwest and California regions (Figure 7c). Alternatively, wildfires were associated with a negligible change or even a decrease in the 0.05^th flow magnitude at 11 streams, mostly found in the Grande Basin and Lower Colorado regions (Figure 7c). The burning of watersheds was also attributed to at least a 10% (S.E. < 10%) increase in flow at the 0.95^th quantile at 16 stream sites (Figure 7d). Across these streams, the median fire-related increase in flow at the 0.95^th quantile for the five post-fire years ranged from 10–161% (S.E. < 10%). The greatest fire enhanced flow at the 0.95^th flow was found at stream sites in the PNW and Missouri regions (Figure 7d). In contrast, fires were associated with a negligible change or even a decrease in the 0.95^th quantile flow magnitude at 28 stream sites, often located in the Rio Grande, Lower Colorado, and Great Basin regions (Figure 7d).

The asymmetry in fire influence on daily flow across quantiles was further interrogated by contrasting the fire-related change (in percent-%) in the 0.05^th and 0.95^th quantile daily flow magnitudes at each stream site (Figure 8). Wildfires were attributed to increases in both the 0.05^th and the 0.95^th quantile daily flow magnitudes (Figure 8, 1^st quadrant) in 17 out of the 44 studied stream sites. These streams were mostly found in the PNW and Missouri regions. In 13 out of these 17 stream sites, the fire-related increase in flow at the 0.05^th quantile was relatively higher than that at the 0.95^th quantile. Fires were also related to higher 0.05^th quantile daily flows and lower 0.95^th quantile daily flows (Figure 8, 4^th quadrant) in 14 streams (Figure 8). These stream sites were often found in the California, Lower Colorado, and Rio Grande regions. Further, fires enhanced the daily flow at the 0.95^th quantiles and reduced the daily flow at the 0.05^th quantiles (Figure 8, 2^nd quadrant) in 6 streams. These stream sites were partially found in the Missouri regions. Finally, fire effects were attributed to lowering the post-fire daily flows at both the 0.05^th and 0.95^th quantiles (3^rd quadrant) in 7 stream sites. Over half of these stream sites were found in the Great Basin and Lower Colorado regions.

Figure 8:

Joint fire-related change (%) in daily flow at the 0.05^th and 0.95^th quantiles across studied streams. In this figure, the length of the arrow represents the total fire-related change (%) in the 0.05^th and 0.95^th quantile daily flows, while the angle of the arrow is the arctangent of ratio of the fire-related change in flow at the 0.95^th quantile and 0.05^th quantile. A vertical (horizontal) arrow indicates that the fire-attributed change in daily stream discharge is only at the 0.95^th (0.05^th) quantile. Arrows at a 45° angle signify that the the fire attributed increase in daily stream discharge at the 0.05^th and 0.95^th quantiles are equal. The color of the arrow represents the quadrant within the $\Delta Q_{\mathit{\text{Fire}}}^{(0.05)}-\Delta Q_{\mathit{\text{Fire}}}^{(0.95)}$ subspace in which it belongs: 1^st quadrant (red), 2^nd quadrant (blue), 3^rd quadrant (dark orchid) and 4^th quadrant (forest green).

Two random forest models were developed to offer insights on the burned watershed attributes that may explain for the difference in the estimated fire effects on the 0.05^th and 0.95^th quantile flow magnitudes across studied streams. These models represented 52% and 25% of the total variability in the median fire-related change in flow at the 0.05^th and 0.95^th quantiles, respectively. Variable importance plot for the flow response at the 0.05^th quantile model (Figure 9a) reveals that soil permeability, average watershed slope, burned watershed and riparian area and severity, and annual baseflow index were the seven most important predictors. Partial dependence plots for this model (Figures 9b–i) show that wildfire’s enhancing effect on the 0.05^th quantile flow magnitude was positively associated with average watershed slope, burned watershed area, riparian area burned under high severity, watershed area burned under high severity, and inversely related to soil permeability, longitude, and annual baseflow index (Figures 9b–i).

Figure 9:

Variable importance (a) and partial dependence (b-i) plots for predictor variables included in the random forest model for fire-related changes (%) in streamflow at the 0.05^th quantile. This model represents 52% of the variability in the fire-related flow change at the 0.05^th quantile across studied stream sites.

Variable importance plot for the 0.95^th quantile flow response model (Figure 10a) reveals that October-March precipitation anomaly, watershed shrub and barren areas, burned watershed and riparian area and severity were the seven most important covariates. Partial dependence plots for this model show that the fire-related increase in the magnitude of flow at the 0.95^th quantile was positively associated with October-March precipitation anomalies, riparian area burned under high severity, riparian burn area, watershed area burned under high severity, watershed area burned, and summer precipitation anomaly, and negatively related to watershed shrub area (Figures 10b–i).

Figure 10:

Variable importance (a) and partial dependence (b-i) plots for predictor variables included in the random forest model for fire-related changes (%) in streamflow at the 0.95^th quantile. This model represents 25% of the variability in the fire-related flow change at the 0.95^th quantile across studied stream sites.

4. Discussion

This study presented a quantile-based framework that entails three empirical approaches to detect and quantify the impact of upland watershed burning on the annual low and peak stream flows while accounting for post-fire weather influences. In this framework, the bootstrap and double mass analysis approaches are used to analyze the difference in the pre-and post-fire streamflow and weather statistics, and the quantile regression approach is used to parse and quantify weather and wildfire effects on annual low and peak flows. The advantage of using this framework is that it only requires pre-and post-fire streamflow data from burned watersheds unlike the traditional paired watershed analysis. Moreover, it can be applied in burned watersheds with just 10 years of pre-and post-fire streamflow data because it (a) does not involve the development of complex models, (b) is mostly non-parametric and thus imposes little assumption about data distribution, and (c) utilizes multiple separate analytical approaches to infer fire effects on low and peak flows, and (d) doesn’t require arbitrary partitioning of data.

The application of this framework on 44 western US streams with burned watersheds indicated that wildfire effects on annual low and peak flows can vary from negligible or reducing to increasing across stream sites. In stream sites with small watershed burns (< 10%), wildfire-related increase in flow at the 0.05^th and 0.95^th quantiles were rarely detected in any of the three methods incorporated in the frame-work. In contrast, wildfire’s enhancing effect on low and peak flows were often found in stream sites with large, high-severity watershed burns, and the quantile regression approach results show that the median fire-related increase in flow for the five post-fire years can be up to 5000% at the 0.05^th quantile and 161% at the 0.95^th quantile. These findings bolster previous arguments that the spatial extent of a wildfire or other forest disturbance at a watershed scale influences whether its signals can be detected on the downstream hydrology (e.g., Stednick, 1996; Wagenbrenner & Robichaud, 2014; Wine & Cadol, 2016; Buma & Livneh, 2017; Hallema et al., 2018). The estimated fire-related changes in daily flow rates at the 0.05^th and 0.95^th quantiles in this study are also comparable to the reported changes in low and peak flows in previous wildfire studies. Kinoshita and Hogue (2015) reported that for two catchments in California with extensive burns, streamflow at the 0.10^th quantile was, on average, 1090% and 118% higher than that of the pre-fire for the ten post-fire years despite not detecting a significant change in the annual precipitation amounts post-fire. Seibert et al. (2010) found that the 1970 wildfire burn at Entiat Experimental Forest was associated with a 120% increase in peak flow magnitudes on average for at least the six following years. Nonetheless, not all large, high severity fires corresponded to increases in flow at the two quantiles at studied streams. This suggests that the watershed pyrology was not the only determinant of the fire-related change in flows at studied watersheds.

Previous studies have shown that post-fire weather conditions can determine the hydrology in watersheds with extensive burns (Moody & Martin, 2001; Owens et al., 2013; Bart, 2016). In our case studies, the direction of post-fire change in flow at the 0.05^th and 0.95^th quantiles corresponded to the direction of change in annual precipitation totals for most streams (Figures 4d and e). The quantile regression results also show that post-fire weather patterns were associated with a change in flow at the 0.05^th and 0.95^th quantiles by up to 230% (SE < 10%), relative to that of the pre-fire (Figures 7a and b). In addition, the two random forest models for streamflow response at 0.95^th quantile indicate that the fire-related change in flow at the 0.95^th quantile was itself strongly influenced by the post-fire October-March precipitation totals (Figure 10b). The importance of weather effects on the total and fire-related change in flow at low and peak flows at our sites may explain why not all high severity fires were associated with higher flow rates at the 0.05^th and 0.95^th quantiles. It also highlights the need to develop empirical methods and frameworks that can account for weather effects on the post-fire flow changes.

Application of the proposed framework on the 44 WUS stream sites also revealed that the enhancing effect of fire on flow was pronounced at the 0.05^th quantile than at the 0.95^th quantile for most of the stream sites in the Pacific Northwest and California regions (Figure 8). This is perhaps because the timing of the annual peak flow events at these stream sites often coincided with the wet and cool seasons of the year (Figure S4), and wet and/or cool weather conditions have been shown to attenuate or even mute fire effects on key hydrological processes such as evapotranspiration (Bart, 2016; Poon & Kinoshita, 2018) and soil hydrophobicity (MacDonald & Huffman, 2004).

In this study, the utility of the proposed quantile-based analytical framework was framed in terms of its use in wildfire-annual low and peak flow studies. However, this framework can also be used to assess the impact of any type of forest or land cover disturbance (e.g., pest, harvesting, dams) on the downslope stream hydrology at a seasonal-to-annual time scale.

Nonetheless, our framework has many weaknesses and applicability issues. One possible limitation is that our framework does not account for a lagged post-fire hydrologic response, stemming from lagged tree mortality, large watershed size, and complex drainage system (Wine, Cadol, & Makhnin, 2018; Wine, Makhnin, & Cadol, 2018). In general, the bootstrap and DMC approaches in our framework can easily be modified to determine if there is a time lag in the post-fire streamflow response. However, resolving for the time lag must also be accompanied by additional analyses to evaluate the source of the lag at a burned watershed, a study that requires separate analyses of its own. So possible users of this analytical framework should be aware of this limitation.

The LOOCV evaluations of our LQR quantile regression models for streamflow at the 0.05th and 0.95th quantiles across studied watersheds indicate that our fire and weather attribution method performs better for peak flows over low flows (Figures 6a–f). This may be because of two factors. Annual low flows generally show lower and/or lagged responses to prevailing weather/climate variability due to contributions from sub-surface storages. Another is in some of our small arid watersheds, annual low flows occur in multiple seasons. This makes the modeling of weather effects using a maximum of two seasonal-to-annual weather variables a challenging task. Thus, in small arid watersheds where the seasonality of low and/or peak flows occurs in multiple seasons, we recommend that our framework be used to assess fire impact on the low and peak flows at a seasonal scale.

Finally, this framework was applied in burned watersheds, where human activities pre-and post-fire were relatively negligible. Furthermore, the selection of watersheds and fire years in this study were made such that multiple wildfire disturbances did not overlap. However, in most WUS watersheds, anthropogenic influence on the hydrology is not minor. Moreover, burn events may immediately be accompanied by other forms of watershed disturbances stemming from phase changes in climate (e.g., Pacific Decadal Oscillation) and natural or anthropogenic induced forest disturbances (e.g., pests, harvesting), complicating its impact on the downslope streamflow. It is acknowledged that the proposed framework in its current form may just lump the impact of overlapping disturbances on the stream hydrology and attribute it to fire effects.

5. Concluding Remarks

The current study presents a quantile- based analytical framework that can be used to detect and quantify fire effects on daily flow at upper and lower quantiles. This has the potential to broaden the scope of wildfire studies by allowing the characterization of fire effects on low and peak flows across many burned sites. In turn, this may afford important insights regarding fire-related flood hazards, which is vital to numerous human-environmental systems. It should also be noted that the nature of post-fire changes in low and peak daily stream flows in the WUS, which occur on the order of half a decade, are embedded on a decadal or longer temporal scale pattern in streamflow in WUS. Many hydrology studies report that over the past 50–100 years, declining trends in snowpack and precipitation amounts due to global climate warming are altering the frequency and magnitude of low and peak flow magnitudes in the western US streams (Lins & Slack, 1999; Rice et al., 2015; Kormos et al., 2016; Dethier et al., 2020). The work here, along with other wildfire studies, suggests that drought and flood hazard diagnostic studies in the WUS could stand to benefit from an improved quantile-based characterization of fire effects daily streamflow, since fire effects on daily stream flows may amplify or ameliorate the long-term trends in low and peak daily streamflow at least on a short time (¡ 10 years) frame.

Key Points:

• Evaluating the impact of watershed burning on the streamflow regime can be problematic due to the confounding effect of postfire weather influences.

• A quantile based analytical framework is presented for assessing fire effect on low & peak flow magnitudes, while accounting for weather influences.

• This analytical framework can be useful for characterizing fire effect on low & peak flows in burned watersheds without overlapping disturbances.

Data Availability Statement

This study uses data that are from online, publicly available national datasets: MTBS (https://www.mtbs.gov/direct-download), GAGES II (https://doi.org/10.5066/F7P55KJN), PRISM (http://www.prism.oregonstate.edu), GRIDMET (https://climatologylab.org/datasets.html), NHDPlus V2 (https://www.epa.gov/waterdata/get-nhdplus-national-hydrography-dataset-plus-data), NLCD 2001 (https://www.mrlc.gov/data/nlcd-2001-land-cover-conus), STATSGO (https://water.usgs.gov/GIS/metadata/usgswrd/XML/ussoils.xml#stdorder), and HYDRO1k Elevation derivative database (https://www.usgs.gov/centers/eros/science/usgs-eros-archive-digital-elevation-hydro1k?qt-science_center_objects=0#qt-science_center_objects)