# Impacts of Spatial Heterogeneity and Temporal Non-Stationarity on Intensity-Duration-Frequency Estimates—A Case Study in a Mountainous California-Nevada Watershed

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Area

#### 2.2. Method

#### 2.3. Trend Analysis

#### 2.4. Quasi-Stationary and Non-Stationary IDFs

#### 2.5. Geostatistics: (Variogram and Kriging)

## 3. Results

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location of the study area on a google map. The red line is the boundary of the Walker River Basin. The dots are the centroid locations of the bias-corrected Regional Earth System Model (RESM) data, with different colors corresponding to the elevations of the grid centroids. The altitude contour in this study domain is illustrated in black lines. The indexed black triangle boxes correspond to the six selected grids with distinct topography for illustration in the results section. The purple cross symbols represent the closest weather stations to each selected grid.

**Figure 2.**Spatial distributions of trending (Sen’s slope) of 126-year precipitation annual maximum series (AMS) for (

**a**) 6-h duration events under representative concentration pathway (RCP)4.5; (

**b**) 24-h duration events under RCP4.5; (

**c**) 6-h duration events under RCP8.5; and (

**d**) 24-h duration events under RCP8.5.

**Figure 3.**Example intensity-duration-frequencies (IDFs) at six selected grids for events with 6-h duration and 2-, 5-, 10-, 25-, 50-, and 100-year return periods, including the estimates from (1) the non-stationary NEVA approach, with the black boxplots showing the uncertainty bounds (here defined by the 1.5 interquartile range (IQR)) of IDF estimates using Non-Stationary Extreme Value Analysis (NEVA); (2) the quasi-stationary estimation during the four time periods: year 1975–2004, year 2011–2040, year 2041–2070 and year 2071–2100, as shown in red, green, blue, and cyan dashed lines, respectively, and (3) the adjacent weather stations (yellow solid lines). The panels (

**a**–

**f**) are for the RCP4.5 scenario; the panels (

**g**–

**l**) are for the RCP8.5 scenario.

**Figure 4.**Example IDFs same as Figure 3, for 24-h durations.

**Figure 5.**The relative differences of precipitation intensities from NEVA non-stationary IDF estimates to those from quasi-stationary IDF analysis, for the historical (1975–2004) and future time periods (2011–2040, 2041–2070, and 2071–2100), for 6- and 24-h duration events with 10-, 25-, 50-, and 100-year return periods, under the RCP4.5 scenario. Each boxplot corresponds to the distribution of estimated precipitation intensity differences across the grids of the entire watershed.

**Figure 6.**Same as Figure 5, but under the RCP8.5 scenario.

**Figure 7.**Spatial precipitation intensity distribution of 6-h duration 100-year events based on the quasi-stationary IDF approach for historical (1975–2004) and future (2011–2040, 2041–2070, and 2071–2100) time periods, and non-stationary estimation. The top row is for the RCP4.5 scenario; the bottom is for the RCP8.5 scenario.

**Figure 8.**The same as Figure 7, but for 24-h duration events.

**Figure 9.**The boxplots of precipitation intensity for 6- and 24-h 100-year events at return period 100-year under different climate scenarios from the IDFs derived from quasi-stationary and non-stationary NEVA estimates, grouped by elevations of all the grids in the study domain.

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**MDPI and ACS Style**

Ren, H.; Hou, Z.J.; Wigmosta, M.; Liu, Y.; Leung, L.R. Impacts of Spatial Heterogeneity and Temporal Non-Stationarity on Intensity-Duration-Frequency Estimates—A Case Study in a Mountainous California-Nevada Watershed. *Water* **2019**, *11*, 1296.
https://doi.org/10.3390/w11061296

**AMA Style**

Ren H, Hou ZJ, Wigmosta M, Liu Y, Leung LR. Impacts of Spatial Heterogeneity and Temporal Non-Stationarity on Intensity-Duration-Frequency Estimates—A Case Study in a Mountainous California-Nevada Watershed. *Water*. 2019; 11(6):1296.
https://doi.org/10.3390/w11061296

**Chicago/Turabian Style**

Ren, Huiying, Z. Jason Hou, Mark Wigmosta, Ying Liu, and L. Ruby Leung. 2019. "Impacts of Spatial Heterogeneity and Temporal Non-Stationarity on Intensity-Duration-Frequency Estimates—A Case Study in a Mountainous California-Nevada Watershed" *Water* 11, no. 6: 1296.
https://doi.org/10.3390/w11061296