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Use Cases

Stream permanence for the contiguous United States

Keywords: probability of zero flows; streamflow; survival regression

Domain: Stream Characteristics

Language: R

Description:

This use case estimates probabilities of detecting at least x days of zero streamflow, where x equals 1, 3, 7, and 30 days, for river locations across the contiguous United States as a function of drainage area. Also included are the 95-percent confidence intervals around the probability estimates. Probabilities are estimated by survival regression models, which are simple, non-parametric, empirically-based models that assume a decreasing probability of observing at least n days of zero streamflow as drainage area increases.

Linked Catalog Datasets:

Use Case: Stream permanence for the contiguous United States

Use Case: Stream permanence for the contiguous United States

Author

Stacey A. Archfield

Published

April 15, 2026

1 Introduction

This workflow applies a non-parametric, empirically-based approach to estimate the probability of observing at least x days of zero streamflow. The results are intended as a minimum-viable product to compliment the streamflow network developed by the 3-Dimensional Hydrography Program (3DHP), which currently only provides a stream network and contributing drainage areas to stream locations in the contiguous United States.

2 Streamgages, data, and methods

2.1 Stream permanence information

Streamgages belonging to the Geospatial Attributes of Gages for Evaluating Streamflow (GAGES-II) dataset (Falcone 2011) were considered for inclusion in this study, regardless of their classification in the dataset as a Reference (having minimal regulation in their upstream catchment area) or Non-Reference (having some combination of water-use, land-use, or the presence of dams in the upstream catchment area) streamgage. Streamgages were required to have at least 10 years of complete, daily streamflow observations for any period of time. For this reason, the approach does not consider if stream permanence has changed over time. This screening resulted in 7,680 streamgages.

Counts of the average annual number of observed zero-flow days were computed for these streamgages. For example, if a streamgage had 10 years of continuous, daily streamflow data, the number of zero-flow days in each of the 10 years was counted and then the average of the 10 annual counts was estimated to obtain the average annual number of zero-flow days for that streamgage.

2.2 Modeling units

In addition to the average annual number of zero-flow days observed, the location of the streamgage in the 2nd-, 4th-, and 8th-level Hydrologic Unit Codes (HUC) Jones et al. (2022) are known. This information is assumed to be a proxy for physiographic and hydroclimatic characteristics that are not yet available in 3DHP.

We initially selected 2nd-level HUCs in the United States as our modeling units. Using additional hydrographic judgement, the modeling units were further refined through the following adjustments:

  1. Second-level HUCs 05 and 06 were combined due to sample sizes, proximity, and size of the HUC 02 areas. This modeling unit was renamed as 05 & 06.

  2. Second-level HUC 03 was subdivided into 3 regions and renamed HUC 03N (North), HUC 03S (South), HUC 03W (West) due to the differences in physiographic and hydroclimatic differences across the HUC 03 area.

  3. Second-level HUC 10 was subdivided into 2 regions and renamed HUC 10U (Upper) and HUC 10L (Lower) to be consistent with the subdivision of HUC 10 in Falcone (2011).

  4. Fourth-level HUC units 1701, 1706 were grouped with HUC 10U due to hydroclimatic differences with other 4th-level HUC units in HUC 17.

  5. Fourth-level HUC units 1704, 1705 were grouped with 2nd-level HUC 16 due to hydroclimatic differences with with other 4th-level HUC units in HUC 17.

Figure 1: Modeling units used to estimate of the probability of observing 1, 3, 7, and 30 days of zero streamflow. Each modeling unit has 4 survivial regression models that relate the contributing drainage area to a river location to the probability of observing 1, 3, 7, and 30 days of zero streamflow.

2.3 Survival regression approach

Survival regression estimates the probability an individual survives past time, t. For our application, we are estimating the probability that at least x days of zero flow are present - or survive - past a certain drainage area value. Survival analysis, therefore, implies that the probability of observing at least x days of zero flow decreases with increasing drainage area.

Survival regression is commonly applied in the health sciences (Hosmer, Lemeshow, and May 2008) but less so in hydrology; in hydrology, it is mainly used with censored data (Helsel 2012). Survival regression allows us to include – but censor – the large number of streamgages where no zero flows are observed (in survival terms, a death was not observed over the period of observation).

From survival regression, we can estimate:

  • The probability of observing at least x days of zero flow, and
  • The 95% confidence interval on this probability.

We apply the Kaplan-Meier estimator of the survival function (Hosmer, Lemeshow, and May 2008). This is an empirical estimate of the probability that depends on a ratio of the number of streamgages for which at least x zero-flow days are observed at a drainage area value and the total number of streamgages remaining (surviving) at each increasing observation of drainage area. The censored values (streamgages for which no zero-flow days were observed) contribute to the total number of streamgages but not to the probability estimates.

As with any regression approach, estimates are limited to the bounds of the training dataset. That is, probability estimates are limited the range of drainage area values under which the models are developed.

Confidence internals are reported for the 95% upper and lower bounds and display asymmetrical behavior because the intervals are computed in log space (as additive errors) and transformed back to real space (where the errors are multiplicative). In survival regression, confidence intervals have been shown to perform well with samples as small as 25 and up to 50-percent censoring, meaning that x days of zero flows are observed in at least half of the streamgages. Warnings are shown for modeling units that have less than 25 streamgages or have greater than 50 percent of the streamgages with no observed zero flow days.

See Hosmer, Lemeshow, and May (2008), Therneau and Grambsch (2000), and Therneau (2024) for more information on survival regression and confidence intervals.

3 Estimates of stream permanence using survival regression

Survival regression curve estimates by modeling unit are graphically shown for the probabilities of observing 1, 3, 7 and 30 days of zero streamflow, on an average annual basis. Look-up tables for each model are located in Archfield et al. (2026; https://doi.org/10.5066/P1BNCITF).

3.1 Probability of observing at least 1 day of zero streamflow

The following survival regression curves for each modeling unit estimate the probability of observing at least 1 day of zero streamflow, on an average annual basis, as a function of drainage area.

Kaplan-Meier survival regression curve for Modeling Unit 01.

14 out of 299 (4.7 percent) streamgages have at least 1 day of zero flow for Modeling Unit 01.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 02.

60 out of 745 (8.1 percent) streamgages have at least 1 day of zero flow for Modeling Unit 02.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03N.

39 out of 334 (11.7 percent) streamgages have at least 1 day of zero flow for Modeling Unit 03N.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03S.

81 out of 205 (39.5 percent) streamgages have at least 1 day of zero flow for Modeling Unit 03S.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03W.

13 out of 280 (4.6 percent) streamgages have at least 1 day of zero flow for Modeling Unit 03W.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 05 & 06.

132 out of 820 (16.1 percent) streamgages have at least 1 day of zero flow for Modeling Unit 05 & 06.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 07.

124 out of 469 (26.4 percent) streamgages have at least 1 day of zero flow for Modeling Unit 07.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 08.

32 out of 141 (22.7 percent) streamgages have at least 1 day of zero flow for Modeling Unit 08.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 09.

46 out of 77 (59.7 percent) streamgages have at least 1 day of zero flow for Modeling Unit 09.

Kaplan-Meier survival regression curve for Modeling Unit 10U.

139 out of 345 (40.3 percent) streamgages have at least 1 day of zero flow for Modeling Unit 10U.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 10L.

171 out of 447 (38.3 percent) streamgages have at least 1 day of zero flow for Modeling Unit 10L.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 11.

228 out of 420 (54.3 percent) streamgages have at least 1 day of zero flow for Modeling Unit 11.

Kaplan-Meier survival regression curve for Modeling Unit 12.

252 out of 361 (69.8 percent) streamgages have at least 1 day of zero flow for Modeling Unit 12.

Kaplan-Meier survival regression curve for Modeling Unit 13.

53 out of 129 (41.1 percent) streamgages have at least 1 day of zero flow for Modeling Unit 13.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 14.

55 out of 329 (16.7 percent) streamgages have at least 1 day of zero flow for Modeling Unit 14.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 15.

94 out of 160 (58.7 percent) streamgages have at least 1 day of zero flow for Modeling Unit 15.

Kaplan-Meier survival regression curve for Modeling Unit 16.

42 out of 232 (18.1 percent) streamgages have at least 1 day of zero flow for Modeling Unit 16.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 17.

76 out of 780 (9.7 percent) streamgages have at least 1 day of zero flow for Modeling Unit 17.

Less than 50% of the streamgages have at least 1 day of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 18.

350 out of 681 (51.4 percent) streamgages have at least 1 day of zero flow for Modeling Unit 18.

3.2 Probability of observing at least 3 days of zero streamflow

The following survival regression curves for each modeling unit estimate the probability of observing at least 3 days of zero streamflow, on an average annual basis, as a function of drainage area.

Kaplan-Meier survival regression curve for Modeling Unit 01.

7 out of 299 (2.3 percent) streamgages have at least 3 days of zero flow for Modeling Unit 01.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 02.

33 out of 745 (4.4 percent) streamgages have at least 3 days of zero flow for Modeling Unit 02.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03N.

29 out of 334 (8.7 percent) streamgages have at least 3 days of zero flow for Modeling Unit 03N.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03S.

69 out of 205 (33.7 percent) streamgages have at least 3 days of zero flow for Modeling Unit 03S.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03W.

9 out of 280 (3.2 percent) streamgages have at least 3 days of zero flow for Modeling Unit 03W.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 05 & 06.

103 out of 820 (12.6 percent) streamgages have at least 3 days of zero flow for Modeling Unit 05 & 06.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 07.

99 out of 469 (21.1 percent) streamgages have at least 3 days of zero flow for Modeling Unit 07.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 08.

28 out of 141 (19.9 percent) streamgages have at least 3 days of zero flow for Modeling Unit 08.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 09.

43 out of 77 (55.8 percent) streamgages have at least 3 days of zero flow for Modeling Unit 09.

Kaplan-Meier survival regression curve for Modeling Unit 10U.

127 out of 345 (36.8 percent) streamgages have at least 3 days of zero flow for Modeling Unit 10U.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 10L.

142 out of 447 (31.8 percent) streamgages have at least 3 days of zero flow for Modeling Unit 10L.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 11.

192 out of 420 (45.7 percent) streamgages have at least 3 days of zero flow for Modeling Unit 11.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 12.

236 out of 361 (65.4 percent) streamgages have at least 3 days of zero flow for Modeling Unit 12.

Kaplan-Meier survival regression curve for Modeling Unit 13.

43 out of 129 (33.3 percent) streamgages have at least 3 days of zero flow for Modeling Unit 13.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 14.

44 out of 329 (13.4 percent) streamgages have at least 3 days of zero flow for Modeling Unit 14.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 15.

90 out of 160 (56.2 percent) streamgages have at least 3 days of zero flow for Modeling Unit 15.

Kaplan-Meier survival regression curve for Modeling Unit 16.

35 out of 232 (15.1 percent) streamgages have at least 3 days of zero flow for Modeling Unit 16.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 17.

65 out of 780 (8.3 percent) streamgages have at least 3 days of zero flow for Modeling Unit 17.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 18.

329 out of 681 (48.3 percent) streamgages have at least 3 days of zero flow for Modeling Unit 18.

Less than 50% of the streamgages have at least 3 days of zero flow. Survival curve estimates may be more uncertain.

3.3 Probability of observing at least 7 days of zero streamflow

The following survival regression curves for each modeling unit estimate the probability of observing at least 7 days of zero streamflow, on an average annual basis, as a function of drainage area.

Kaplan-Meier survival regression curve for Modeling Unit 01.

3 out of 299 (1 percent) streamgages have at least 7 days of zero flow for Modeling Unit 01.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 02.

23 out of 745 (3.1 percent) streamgages have at least 7 days of zero flow for Modeling Unit 02.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03N.

21 out of 334 (6.3 percent) streamgages have at least 7 days of zero flow for Modeling Unit 03N.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03S.

54 out of 205 (26.3 percent) streamgages have at least 7 days of zero flow for Modeling Unit 03S.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03W.

7 out of 280 (2.5 percent) streamgages have at least 7 days of zero flow for Modeling Unit 03W.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 05 & 06.

75 out of 820 (9.1 percent) streamgages have at least 7 days of zero flow for Modeling Unit 05 & 06.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 07.

71 out of 469 (15.1 percent) streamgages have at least 7 days of zero flow for Modeling Unit 07.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 08.

18 out of 141 (12.8 percent) streamgages have at least 7 days of zero flow for Modeling Unit 08.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 09.

40 out of 77 (51.9 percent) streamgages have at least 7 days of zero flow for Modeling Unit 09.

Kaplan-Meier survival regression curve for Modeling Unit 10U.

109 out of 345 (31.6 percent) streamgages have at least 7 days of zero flow for Modeling Unit 10U.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 10L.

112 out of 447 (25.1 percent) streamgages have at least 7 days of zero flow for Modeling Unit 10L.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 11.

160 out of 420 (38.1 percent) streamgages have at least 7 days of zero flow for Modeling Unit 11.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 12.

212 out of 361 (58.7 percent) streamgages have at least 7 days of zero flow for Modeling Unit 12.

Kaplan-Meier survival regression curve for Modeling Unit 13.

41 out of 129 (31.8 percent) streamgages have at least 7 days of zero flow for Modeling Unit 13.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 14.

39 out of 329 (11.9 percent) streamgages have at least 7 days of zero flow for Modeling Unit 14.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 15.

83 out of 160 (51.9 percent) streamgages have at least 7 days of zero flow for Modeling Unit 15.

Kaplan-Meier survival regression curve for Modeling Unit 16.

30 out of 232 (12.9 percent) streamgages have at least 7 days of zero flow for Modeling Unit 16.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 17.

56 out of 780 (7.2 percent) streamgages have at least 7 days of zero flow for Modeling Unit 17.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 18.

310 out of 681 (45.5 percent) streamgages have at least 7 days of zero flow for Modeling Unit 18.

Less than 50% of the streamgages have at least 7 days of zero flow. Survival curve estimates may be more uncertain.

3.4 Probability of observing at least 30 days of zero streamflow

The following survival regression curves for each modeling unit estimate the probability of observing at least 30 days of zero streamflow, on an average annual basis, as a function of drainage area.

Kaplan-Meier survival regression curve for Modeling Unit 01.

0 out of 299 (0 percent) streamgages have at least 30 days of zero flow for Modeling Unit 01.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 02.

6 out of 745 (0.8 percent) streamgages have at least 30 days of zero flow for Modeling Unit 02.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03N.

2 out of 334 (0.6 percent) streamgages have at least 30 days of zero flow for Modeling Unit 03N.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03S.

32 out of 205 (15.6 percent) streamgages have at least 30 days of zero flow for Modeling Unit 03S.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 03W.

0 out of 280 (0 percent) streamgages have at least 30 days of zero flow for Modeling Unit 03W.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 05 & 06.

20 out of 820 (2.4 percent) streamgages have at least 30 days of zero flow for Modeling Unit 05 & 06.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 07.

36 out of 469 (7.7 percent) streamgages have at least 30 days of zero flow for Modeling Unit 07.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 08.

7 out of 141 (5 percent) streamgages have at least 30 days of zero flow for Modeling Unit 08.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 09.

24 out of 77 (31.2 percent) streamgages have at least 30 days of zero flow for Modeling Unit 09.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 10U.

73 out of 345 (21.2 percent) streamgages have at least 30 days of zero flow for Modeling Unit 10U.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 10L.

66 out of 447 (14.8 percent) streamgages have at least 30 days of zero flow for Modeling Unit 10L.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 11.

88 out of 420 (21 percent) streamgages have at least 30 days of zero flow for Modeling Unit 11.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 12.

144 out of 361 (39.9 percent) streamgages have at least 30 days of zero flow for Modeling Unit 12.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 13.

35 out of 129 (27.1 percent) streamgages have at least 30 days of zero flow for Modeling Unit 13.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 14.

21 out of 329 (6.4 percent) streamgages have at least 30 days of zero flow for Modeling Unit 14.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 15.

69 out of 160 (43.1 percent) streamgages have at least 30 days of zero flow for Modeling Unit 15.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 16.

13 out of 232 (5.6 percent) streamgages have at least 30 days of zero flow for Modeling Unit 16.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 17.

33 out of 780 (4.2 percent) streamgages have at least 30 days of zero flow for Modeling Unit 17.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

Kaplan-Meier survival regression curve for Modeling Unit 18.

241 out of 681 (35.4 percent) streamgages have at least 30 days of zero flow for Modeling Unit 18.

Less than 50% of the streamgages have at least 30 days of zero flow. Survival curve estimates may be more uncertain.

4 References Cited

Falcone, James. 2011. “GAGES-II: Geospatial Attributes of Gages for Evaluating Streamflow.” Reston, VA. http://pubs.er.usgs.gov/publication/70046617.
Helsel, Dennis R. 2012. Statistics for Censored Environmental Data Using Minitab and r. 2nd Edition. Vol. 77. John Wiley & Sons.
Hosmer, David W., Stanley Lemeshow, and Susanne May. 2008. Applied Survival Analysis: Regression Modeling of Time-to-Event Data. John Wiley & Sons, Ltd. https://doi.org/10.1002/9780470258019.fmatter.
Jones, K. A., L. S. Niknami, S. G. Buto, and D. Decker. 2022. “Federal Standards and Procedures for the National Watershed Boundary Dataset (WBD) (5 Ed.).” https://pubs.usgs.gov/tm/11/a3/.
Seaber, Paul R., F. Paul Kapinos, and George L. Knapp. 1987. “Hydrologic Unit Maps.” https://pubs.usgs.gov/wsp/wsp2294/.
Therneau, Terry M. 2024. A Package for Survival Analysis in r. https://CRAN.R-project.org/package=survival.
Therneau, Terry M., and Patricia M. Grambsch. 2000. Modeling Survival Data: Extending the Cox Model. New York: Springer.