Corrigendum to: “Low Streamflows in Massachusetts: Variability Over Space and Time and Relations With Climatic and Basin Variables”

Abstract

Chamberlin, C. A. and G. A. Hodgkins (2026). “ Low Streamflows in Massachusetts: Variability Over Space and Time and Relations With Climatic and Basin Variables.” Journal of the American Water Resources Association 62(2). https://doi.org/10.1111/1752-1688.70108

In the original manuscript, it was stated that linear regression models used for various analyses “needed to show linearity and have homoscedastic and normally distributed residuals (p < 0.1 for a non-constant error variance test and a Shapiro–Wilk test).” In fact, homoscedasticity is associated with p > 0.1 in the non-constant error variance test, and normally distributed residuals are associated with p > 0.1 in the Shapiro–Wilk test. These criteria of p > 0.1 for these two tests were met by some, but not all, of the linear regressions presented in the manuscript. Specifically, the models presented in sections 4.2 and 4.3 had p < 0.1 for both tests, so in fact did not meet the criteria of normal distributions and homoscedasticity, while the models presented in section 4.4 had p > 0.1 for both tests and did meet the criteria of normal distributions and homoskedasticity. Heteroskedasticity and nonlinearly distributed residuals can indicate that the relationship between predictor and response variables is not fully linear, and so a linear regression model may over or understate the importance of predictor variables on the response variables. As stated in the original article, we tested other models prior to choosing linear regression and did not find other non-linear models to perform better (adjusted R² values were similar; tested models included Cubist regression models, Random Forest modeling, Poisson regressions, quasi-Poisson regressions, and Tobit regressions).

Updates related to results in sections 4.2 and 4.3 are presented below.

Section 4.2.C

Figure C1: Residual plots for the 6 models presented in Section 4.2, Tables 1–3, and Figures 5–6, including the models for (A) Q2, (B) Q2/Q50, (C) Duration Q2, (D) Q10, (E) Q10/Q50, and (F) Duration Q10. The dashed green line represents a slope of -1, or instances in which the observed value was 0. * indicates a cube root transformation

Section 4.3.C

Results for the second paragraph of section 4.3 can be rewritten with updated Tables C1–C6 that include models that meet the p > 0.1 criteria for linearity and homoscedasticity. These new results broadly support the same conclusions of the previous tables S1–S6, that generating reliable models for individual drought years was difficult, and no clear patterns emerge. The most notable difference between Tables C1–C6 and Tables S1–S6 is that fewer P/PET variables and more temperature and precipitation variables are used for climate variables. Changes to the paragraph from the original text are in bold italics.

For the magnitude models, simpler models with similar adjusted R² values were produced for both Q2 and Q10 in 2016, 2020, and 2022, using combinations of explanatory variables including basin area, sand and gravel, B/C soils, D soils, water/wetland area, population density, reservoir storage, dam density, November–April P/PET, precipitation, and temperature, May-June P/PET and precipitation, and July–August temperature (Tables C1 and C2). For magnitude metrics in other drought years, a satisfactory simple model could not be produced. For normalized magnitudes, simpler models were produced for 2016, 2020, and 2022 for Q2/Q50 and Q10/Q50, and also in 1966 and 1985 for Q2/Q50 using combinations of the explanatory variables basin area, sand and gravel, B/C soils, water/wetlands area, agricultural area, population density, diversions (Boolean variable), reservoir storage, dam density, November-April P/PET and precipitation, May–June temperature and precipitation, July-August precipitation, and September-October precipitation (Tables C3 and C4). Satisfactory models could not be produced for the other years. For durations of low flows, simpler models were produced for durQ2 in 1965 and 2016, and for durQ10 in 1965, 1966, and 1985 (Tables C5 and C6). Explanatory variables for durations of low flows in declared drought years included combinations of water/wetlands area, developed area, population density, reservoir storage, water withdrawals, May-June temperature, July-August precipitation, and September-October temperature.