Investigating Spatial Dependence in the Degree of Asymptotic Dependence between a Satellite Precipitation Product and Station Data in the Northern US Rocky Mountains
Pub. online: 12 March 2026
Type: Data Science In Action
Open Access
Open Access
Received
15 August 2025
15 August 2025
Accepted
11 February 2026
11 February 2026
Published
12 March 2026
12 March 2026
Abstract
Satellite precipitation products have the potential to be employed for the purpose of better understanding extreme precipitation events in remote mountainous terrain, where weather stations and radar data tend to be sparse. For this reason, it is crucial to assess how closely satellite estimates agree with ground observations during extreme events, and how that agreement varies across such regions. We use asymptotic dependence from multivariate extreme value theory as the primary tool in this study. After presenting two measures of asymptotic dependence and their associated estimators, we illustrate these ideas using simulated data. We then model the level of asymptotic dependence between PERSIANN-CDR and SNOTEL station data over the US Northern Rocky Mountains. We consider both asymptotic dependence estimators, and based on hypothesis tests and visual diagnostics, both estimates of asymptotic dependence indicate positive spatial dependence. We also investigate whether geographical factors influence the levels of asymptotic dependence over this region. Using a spatial correlation analysis, we find that elevation is negatively correlated with both asymptotic dependence estimators and average summer temperature is positively correlated with both asymptotic dependence estimators. However, we did not find any geographical covariates to be statistically significant in the model.
Supplementary material
Supplementary MaterialThe authors have compiled a GitHub repository that contains files and data related to this manuscript, that is publicly available and located at https://github.com/brooktrussell/InvestInvestigatingSpatialDependence. More specifically, this repository contains the following materials:
1.
Analysis.R — the R file that contains the code used in this analysis,
2.
Objects.RData — an R workspace file that contains the data used in this analysis,
3.
PRISMelevation — an R workspace file that contains the PRISM data used in this analysis, and
4.
SimStudyCode.R — the R file that contains the code used in the simulation study.
References
Ashouri H, Hsu KL, Sorooshian S, Braithwaite DK, Knapp KR, Cecil LD, et al. (2015). PERSIANN-CDR: Daily precipitation climate data record from multisatellite observations for hydrological and climate studies. Bulletin of the American Meteorological Society, 96(1): 69–83. https://doi.org/10.1175/BAMS-D-13-00068.1
Bharti V, Singh C (2015). Evaluation of error in TRMM 3B42V7 precipitation estimates over the Himalayan region. Journal of Geophysical Research: Atmospheres, 120(24): 12458–12473. https://doi.org/10.1002/2015JD023779
Coles S, Heffernan J, Tawn J (1999). Dependence measures for extreme value analyses. Extremes, 2(4): 339–365. https://doi.org/10.1023/A:1009963131610
Cooley D, Thibaud E (2019). Decompositions of dependence for high-dimensional extremes. Biometrika, 106(3): 587–604. https://doi.org/10.1093/biomet/asz028
Derin Y, Yilmaz KK (2014). Evaluation of multiple satellite-based precipitation products over complex topography. Journal of Hydrometeorology, 15(4): 1498–1516. https://doi.org/10.1175/JHM-D-13-0191.1
Engelke S, Hitz AS (2020). Graphical models for extremes. Journal of the Royal Statistical Society, Series B, Statistical Methodology, 82(4): 871–932. https://doi.org/10.1111/rssb.12355
Gong Y, Zhong P, Opitz T, Huser R (2024). Partial tail-correlation coefficient applied to extremal-network learning. Technometrics, 66(3): 331–346. https://doi.org/10.1080/00401706.2024.2304334
Hirpa FA, Gebremichael M, Hopson T (2010). Evaluation of high-resolution satellite precipitation products over very complex terrain in Ethiopia. Journal of Applied Meteorology and Climatology, 49(5): 1044–1051. https://doi.org/10.1175/2009JAMC2298.1
Huang WK, Cooley DS, Ebert-Uphoff I, Chen C, Chatterjee S (2019). New exploratory tools for extremal dependence: χ networks and annual extremal networks. Journal of Agricultural, Biological, and Environmental Statistics, 24(3): 484–501. https://doi.org/10.1007/s13253-019-00356-4
Huser R, Wadsworth JL (2022). Advances in statistical modeling of spatial extremes. Wiley Interdisciplinary Reviews: Computational Statistics, 14(1): e1537. https://doi.org/10.1002/wics.1537
Jiang Y, Cooley D, Wehner MF (2020). Principal component analysis for extremes and application to US precipitation. Journal of Climate, 33(15): 6441–6451. https://doi.org/10.1175/JCLI-D-19-0413.1
Larsson M, Resnick SI (2012). Extremal dependence measure and extremogram: The regularly varying case. Extremes, 15(2): 231–256. https://doi.org/10.1007/s10687-011-0135-9
Moran PA (1950). Notes on continuous stochastic phenomena. Biometrika, 37(1/2): 17–23. https://doi.org/10.1093/biomet/37.1-2.17
Resnick S (2004). The extremal dependence measure and asymptotic independence. Stochastic Models, 20(2): 205–227. https://doi.org/10.1081/STM-120034129
Russell BT, Cooley DS, Porter WC, Reich BJ, Heald CL (2016). Data mining to investigate the meteorological drivers for extreme ground level ozone events. Annals of Applied Statistics, 10(3): 1673–1698. https://doi.org/10.1214/16-AOAS954
Russell BT, Ding Y, Huang WK, Dyer JL (2024). Characterizing asymptotic dependence between a satellite precipitation product and station data in the northern US Rocky Mountains via the tail dependence regression framework with a Gibbs posterior inference approach. Environmetrics, 35(8): e2890. https://doi.org/10.1002/env.2890
Russell BT, Hogan P (2018). Analyzing dependence matrices to investigate relationships between National Football League Combine event performances. Journal of Quantitative Analysis in Sports, 14(4): 201–212. https://doi.org/10.1515/jqas-2017-0086
Wadsworth JL, Campbell R (2024). Statistical inference for multivariate extremes via a geometric approach. Journal of the Royal Statistical Society Series B: Statistical Methodology, 86(5): 1243–1265. https://doi.org/10.1093/jrsssb/qkae030
