# Projecting Health Impacts of Future Temperature: A Comparison of Quantile-Mapping Bias-Correction Methods

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Metrorology and Health Data

#### 2.2. Bias Correction with Quantile Mapping

#### 2.2.1. Normal Distribution Mapping

#### 2.2.2. Empirical Quantile Mapping

#### 2.2.3. Empirical Robust Quantile Mapping

#### 2.2.4. Quantile Mapping with Linear Transformation Function

#### 2.2.5. Quantile Delta Mapping (QDM)

#### 2.2.6. Application to NA-CORDEX and Evaluations

^{m}and σ

^{0}are the standard deviation of the modeled and observed datasets, respectively.

#### 2.3. Health Effect Estimation and Projection

_{t,H}and AN

_{t,P}over the desired comparison time periods.

_{t,H}and AN

_{t,P}involved nonlinear functions of the estimated log relative risk. We obtained point-projection and projection uncertainty intervals via Monte Carlo simulations. Specifically, we first simulated 5000 realizations of the exposure-response function $f\left(\xb7\right)$ by simulating its spline coefficients from a multivariate Normal distribution with their point estimate as means and the asymptotic covariance matrix. These simulations were then combined with projected future temperature time series to perform uncertainty quantification. We report the median as the point projection estimate, and 95% uncertainty intervals were based on the 2.5th and 97.5th quantile of the simulated health-impact projections.

## 3. Results

_{0}) at 7.07 °C. Figure 3 summarizes excess temperature-related ED visits in the 2050s and 2090s, after applying bias correction with QDM. The number of excess temperature-related ED visits in the 2090s are projected to be higher than that in the 2050s within the same RCM/GCM combination. The projection uncertainty also increased from the 2050s to 2090s. Based on 5000 Monte Carlo simulations from the 10 RCM/GCM combinations, the pooled ensemble approach projected excess temperature-related ED visits per year as 2510 (95% PI: 700–5000) in the 2050s and 5900 (95% PI: 1000–11700) in the 2090s. Without incorporating between-model variability, the average ensemble approach gave similar point projection but slightly small projection intervals. In the sensitivity analysis of alternative health models (Table S2), the pooled projections of annual excess ED visits are similar and have considerable overlap in projection intervals.

## 4. Discussion

_{t}with its projected values.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Woodward, A.; Smith, K.R.; Campbell-Lendrum, D.; Chadee, D.D.; Honda, Y.; Liu, Q.; Olwoch, J.; Revich, B.; Sauerborn, R.; Chafe, Z.; et al. Climate change and health: On the latest IPCC report. Lancet
**2014**, 383, 1185–1189. [Google Scholar] [CrossRef] - Wuebbles, D.J.; Fahey, D.W.; Hibbard, K.A.; Dokken, D.J.; Stewart, B.C.; Maycock, T.K. Climate Science Special Report: Fourth National Climate Assessment, Volume I; U.S. Global Change Research Program: Washington, DC, USA, 2017; p. 470. [Google Scholar]
- Frumkin, H.; Hess, J.; Luber, G.; Malilay, J.; McGeehin, M. Climate change: The public health response. Am. J. Publ. Health
**2008**, 98, 435–445. [Google Scholar] [CrossRef] [PubMed] - Vicedo-Cabrera, A.M.; Sera, F.; Gasparrini, A. Hands-on Tutorial on a Modeling Framework for Projections of Climate Change Impacts on Health. Epidemiology
**2019**, 30, 321–329. [Google Scholar] [CrossRef][Green Version] - Sanderson, M.; Arbuthnott, K.; Kovats, S.; Hajat, S.; Falloon, P. The use of climate information to estimate future mortality from high ambient temperature: A systematic literature review. PLoS ONE
**2017**, 12, e0180369. [Google Scholar] [CrossRef][Green Version] - Räisänen, J.; Räty, O. Projections of daily mean temperature variability in the future: Cross-validation tests with ENSEMBLES regional climate simulations. Clim. Dyn.
**2012**, 41, 1553–1568. [Google Scholar] [CrossRef] - Thrasher, B.; Maurer, E.P.; McKellar, C.; Duffy, P.B. Technical Note: Bias correcting climate model simulated daily temperature extremes with quantile mapping. Hydrol. Earth Syst. Sci.
**2012**, 16, 3309–3314. [Google Scholar] [CrossRef][Green Version] - Teutschbein, C.; Seibert, J. Bias correction of regional climate model simulations for hydrological climate-change impact studies: Review and evaluation of different methods. J. Hydrol.
**2012**, 456–457, 12–29. [Google Scholar] [CrossRef] - Fang, G.H.; Yang, J.; Chen, Y.N.; Zammit, C. Comparing bias correction methods in downscaling meteorological variables for a hydrologic impact study in an arid area in China. Hydrol. Earth Syst. Sci.
**2015**, 19, 2547–2559. [Google Scholar] [CrossRef][Green Version] - Worku, G.; Teferi, E.; Bantider, A.; Dile, Y.T. Statistical bias correction of regional climate model simulations for climate change projection in the Jemma sub-basin, upper Blue Nile Basin of Ethiopia. Theor. Appl. Climatol.
**2019**, 139, 1569–1588. [Google Scholar] [CrossRef] - Azmat, M.; Qamar, M.U.; Huggel, C.; Hussain, E. Future climate and cryosphere impacts on the hydrology of a scarcely gauged catchment on the Jhelum river basin, Northern Pakistan. Sci. Total Environ.
**2018**, 639, 961–976. [Google Scholar] [CrossRef] - Ghimire, U.; Srinivasan, G.; Agarwal, A. Assessment of rainfall bias correction techniques for improved hydrological simulation. Int. J. Climatol.
**2018**, 39, 2386–2399. [Google Scholar] [CrossRef] - Zhou, J.; Chang, H.H.; Fuentes, M. Estimating the Health Impact of Climate Change with Calibrated Climate Model Output. J. Agric. Biol. Environ. Stat.
**2012**, 17, 377–394. [Google Scholar] [CrossRef] - Murari, K.K.; Ghosh, S.; Patwardhan, A.; Daly, E.; Salvi, K. Intensification of future severe heat waves in India and their effect on heat stress and mortality. Reg. Environ. Chang.
**2014**, 15, 569–579. [Google Scholar] [CrossRef] - Guo, Y.; Li, S.; Liu, L.; Chen, D.; Williams, G.; Tong, S. Projecting future temperature-related mortality in three largest Australian cities. Environ. Pollut.
**2016**, 208, 66–73. [Google Scholar] [CrossRef] - Dai, A. Recent climatology, variability, and trends in global surface humidity. J. Clim.
**2006**, 19, 3589–3606. [Google Scholar] [CrossRef][Green Version] - DeGaetano, A.T.; Brown, P.J. Trends in U.S. surface humidity, 1930–2010. J. Appl. Meteorol. Climatol.
**2013**, 52, 147–163. [Google Scholar] [CrossRef] - Chen, K.; Fiore, A.M.; Chen, R.; Jiang, L.; Jones, B.; Schneider, A.; Peters, A.; Bi, J.; Kan, H.; Kinney, P.L. Future ozone-related acute excess mortality under climate and population change scenarios in China: A modeling study. PloS Med.
**2018**, 15, e1002598. [Google Scholar] [CrossRef] [PubMed] - Di Napoli, C.; Pappenberger, F.; Cloke, H.L. Verification of Heat Stress thresholds for a health-based heat-wave definition. J. Appl. Meteorol. Climatol.
**2019**, 58, 1177–1194. [Google Scholar] [CrossRef] - Loughnan, M.E.; Nicholls, N.; Tapper, N.J. The effects of summer temperature, age and socioeconomic circumstance on Acute Myocardial Infarction admissions in Melbourne, Australia. Int. J. Health Geogr.
**2010**, 9. [Google Scholar] [CrossRef][Green Version] - Murage, P.; Hajat, S.; Kovats, R.S. Effect of night-time temperatures on cause and age-specific mortality in London. Environ. Epidemiol.
**2017**. [Google Scholar] [CrossRef] [PubMed] - Karmalkar, A.V. Interpreting results from the NARCCAP and NA-cordex ensembles in the context of uncertainty in regional climate change projections. Bull. Am. Meteorol. Soc.
**2018**, 99, 2093–2106. [Google Scholar] [CrossRef] - Piani, C.; Weedon, G.P.; Best, M.; Gomes, S.M.; Viterbo, P.; Hagemann, S.; Haerter, J.O. Statistical bias correction of global simulated daily precipitation and temperature for the application of hydrological models. J. Hydrol.
**2010**, 395, 199–215. [Google Scholar] [CrossRef] - Gudmundsson, L.; Bremnes, J.B.; Haugen, J.E.; Engen-Skaugen, T. Technical note: Downscaling RCM precipitation to the station scale using statistical transformations—A comparison of methods. Hydrol. Earth Syst. Sci.
**2012**, 16, 3383–3390. [Google Scholar] [CrossRef][Green Version] - Panofsky, H.A. Some Applications of Statistics to Meteorology; Earth and Mineral Sciences Continuing Education, College of Earth and Mineral Sciences, Pennsylvania State University: Philadelphia, PA, USA, 1968; p. 224. [Google Scholar]
- Villani, V.; Rianna, G.; Mercogliano, P.; Zollo, A.L.; Schiano, P. Statistical approaches versus weather generator to downscale rcm outputs to point scale: A comparison of performances. J. Urb. Environ. Eng.
**2015**, 142–154. [Google Scholar] [CrossRef][Green Version] - Boé, J.; Terray, L.; Habets, F.; Martin, E. Statistical and dynamical downscaling of the Seine basin climate for hydro-meteorological studies. Int. J. Climatol.
**2007**, 27, 1643–1655. [Google Scholar] [CrossRef] - Murdock, T.Q.; Sobie, S.R.; Cannon, A.J. Bias Correction of GCM precipitation by quantile mapping: How well do methods preserve changes in quantiles and extremes? J. Clim.
**2015**, 28, 6938–6959. [Google Scholar] [CrossRef] - Tong, Y.; Gao, X.; Han, Z.; Xu, Y.; Xu, Y.; Giorgi, F. Bias correction of temperature and precipitation over China for RCM simulations using the QM and QDM methods. Clim. Dyn.
**2020**. [Google Scholar] [CrossRef] - Chu, X.; Hejabi, S.; Bazrafshan, J.; Bozorg-Haddad, O.; Enayati, M. Bias correction capabilities of quantile mapping methods for rainfall and temperature variables. J. Water Clim. Chang.
**2020**. [Google Scholar] [CrossRef] - Kouhestani, S.; Eslamian, S.S.; Abedi-Koupai, J.; Besalatpour, A.A. Projection of climate change impacts on precipitation using soft-computing techniques: A case study in Zayandeh-rud Basin, Iran. Glob. Planet. Chang.
**2016**, 144, 158–170. [Google Scholar] [CrossRef] - Switanek, M.B.; Troch, P.A.; Castro, C.L.; Leuprecht, A.; Chang, H.-I.; Mukherjee, R.; Demaria, E.M.C. Scaled distribution mapping: A bias correction method that preserves raw climate model projected changes. Hydrol. Earth Syst. Sci.
**2017**, 21, 2649–2666. [Google Scholar] [CrossRef][Green Version] - Ngai, S.T.; Tangang, F.; Juneng, L. Bias correction of global and regional simulated daily precipitation and surface mean temperature over Southeast Asia using quantile mapping method. Glob. Planet. Chang.
**2017**, 149, 79–90. [Google Scholar] [CrossRef][Green Version] - Heo, J.-H.; Ahn, H.; Shin, J.-Y.; Kjeldsen, T.R.; Jeong, C. Probability Distributions for a Quantile Mapping Technique for a Bias Correction of Precipitation Data: A Case Study to Precipitation Data Under Climate Change. Water
**2019**, 11, 1475. [Google Scholar] [CrossRef][Green Version] - Reiter, P.; Gutjahr, O.; Schefczyk, L.; Heinemann, G.; Casper, M. Bias correction of ENSEMBLES precipitation data with focus on the effect of the length of the calibration period. Meteorol. Z.
**2016**, 25, 85–96. [Google Scholar] [CrossRef]

**Figure 1.**Monthly average minimum temperature in Atlanta (2051–2099) for 10 climate models with and without different quantile mapping bias-correction methods. Each color indicates a different GCM and RCM combination from NA-CORDEX. (

**a**) Future monthly mean without correction; (

**b**) Future monthly mean by linear QM; (

**c**) Future monthly mean by empirical QM; (

**d**) Future monthly mean by robust QM; (

**e**) Future monthly mean by normal mapping; (

**f**) Future monthly mean by QDM.

**Figure 2.**Estimated nonlinear associations between 3-day moving averages of minimum temperature on all internal-cause emergency department visits in Atlanta, 1993 to 2004. The exposure-response function has a reference temperature of 7.07 °C, and dotted lines denote the 95% pointwise confidence interval bounds.

**Figure 3.**Projected excess temperature-related ED visits per year and projecquantile delta mapping. Specific global-climate model and regional-climate model combinations from NA-CORDEX are given as M1, M2, …, M10 in Table 1. (

**a**) Excess ED per year (2050–2059); (

**b**) Excess ED per year (2090–2099).

**Table 1.**Ten combinations of global climate models (GCM) and regional climate models (RCM) from the North American-Coordinated Regional Climate Downscaling Experiment (NA-CORDEX) used in this study. Mean bias error (MBE), mean absolute error (MAE), root mean square error (RMSE), and normalized standard deviation (NSD) in °C are between model simulations and airport observations during 1993 to 2004.

Model Index | GCM | RCM | MBE | MAE | RMSE | NSD |
---|---|---|---|---|---|---|

M1 | HadGEM2-ES | WRF | −0.55 | 4.66 | 6.26 | 1.06 |

M2 | CanESM2 | CRCM5-UQAM | 0.88 | 4.68 | 6.16 | 1.03 |

M3 | MPI-ESM-LR | WRF | −0.88 | 4.81 | 6.49 | 1.10 |

M4 | MPI-ESM-LR | RegCM4 | −2.22 | 4.95 | 6.47 | 1.10 |

M5 | GFDL-ESM2M | WRF | −2.25 | 4.98 | 6.53 | 1.05 |

M6 | GFDL-ESM2M | RegCM4 | −3.40 | 5.48 | 7.11 | 1.08 |

M7 | CanESM2 | CanRCM4 | 0.75 | 4.71 | 6.26 | 1.01 |

M8 | MPI-ESM-MR | CRCM5-UQAM | 0.18 | 4.97 | 6.53 | 1.01 |

M9 | EC-EARTH | RCA4 | −0.98 | 4.67 | 6.02 | 0.88 |

M10 | EC-EARTH | HIRHAM5 | 0.60 | 4.45 | 5.94 | 0.92 |

**Table 2.**Comparison of raw and quantile-mapping (QM) bias-corrected climate model simulations. Mean bias error (MBE), mean absolute error (MAE), root mean square error (RMSE), and normalized standard deviation (NSD) in °C were between model simulations and airport observations during 1993 to 2004 and averaged across climate models.

Metric | Raw | Linear QM | Empirical QM | Robust QM | Normal Mapping | QDM |
---|---|---|---|---|---|---|

MBE ($\mathbf{\times}\mathbf{10})$ | −7.86 | −0.00 | 0.02 | 0.01 | 0.02 | 0.00 |

MAE | 4.84 | 4.36 | 4.35 | 4.35 | 4.37 | 4.35 |

RMSE | 6.38 | 5.78 | 5.78 | 5.78 | 5.80 | 5.78 |

NSD | 1.02 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |

**Table 3.**Average between-model standard deviation (SD) for projected daily minimum temperature and excess emergency department (ED) visits in Atlanta between May and September for two projection periods. Statistics were first calculated across days within each climate model and then across 10 models from NA-CORDEX.

Quantile-Mapping Methods | Future Min Temperature (SD Across Climate Models) | Future Excess Ed Visits (SD Across Climate Models) | ||
---|---|---|---|---|

2050–2059 | 2090–2099 | 2050–2059 | 2090–2099 | |

Raw | 1.51 | 1.80 | 2580 | 2889 |

Linear QM | 0.58 | 0.85 | 958 | 1400 |

Empirical QM | 0.68 | 0.82 | 1139 | 1341 |

Robust QM | 0.68 | 0.84 | 1135 | 1331 |

Normal Mapping | 0.58 | 0.86 | 970 | 1424 |

QDM | 0.44 | 0.78 | 723 | 1356 |

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**MDPI and ACS Style**

Qian, W.; Chang, H.H. Projecting Health Impacts of Future Temperature: A Comparison of Quantile-Mapping Bias-Correction Methods. *Int. J. Environ. Res. Public Health* **2021**, *18*, 1992.
https://doi.org/10.3390/ijerph18041992

**AMA Style**

Qian W, Chang HH. Projecting Health Impacts of Future Temperature: A Comparison of Quantile-Mapping Bias-Correction Methods. *International Journal of Environmental Research and Public Health*. 2021; 18(4):1992.
https://doi.org/10.3390/ijerph18041992

**Chicago/Turabian Style**

Qian, Weijia, and Howard H. Chang. 2021. "Projecting Health Impacts of Future Temperature: A Comparison of Quantile-Mapping Bias-Correction Methods" *International Journal of Environmental Research and Public Health* 18, no. 4: 1992.
https://doi.org/10.3390/ijerph18041992