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Characterization of annual urban air temperature changes with special reference to the city of Modena: a comparison between regression models and a proposal for a new index to evaluate relationships between environmental variables

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Abstract

It is commonly recognized that the observed increase in global mean annual air temperature is strongly related to the increase in global carbon dioxide concentration C, and that both these variables are related to global development. It remains, however, unclear the degree to which local mean annual urban air temperature T is affected by local variables such as annual precipitation depth P and urban area extent A. This study assumes that A is a proxy of local development and C is a proxy of global development and investigates the commingled effects of A, P, and C on T by using long-term annual data observed over the years 1881–2019 from the Modena Observatory in Italy. Linear relationships between T, C and A are found to be spurious since all these series have a monotonic increasing trend with time. Parametric analytic models like logistic functions are found to lack flexibility. Smoothing splines can only give insights into the strength of the relationships but not on their shape defining the functional relationship between variables. Advanced nonlinear models like generalized additive models, instead, are found to combine flexibility in a parametric form, and appear therefore to be suitable models for explaining the complex relationships between A, P, and C on T. The different models are evaluated using traditional goodness of fit statistics like R2, AIC, BIC, and a new index of relation IR which is introduced to jointly evaluate the goodness-of-fit of relationships between variables that may either be dependent or independent.

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Data availability

Data sets used in this study are available at https://doi.org/10.1594/PANGAEA.938740.

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Acknowledgements

Air temperature and precipitation time series of Modena were provided by the Geophysical Observatory of the University of Modena and Reggio Emilia, Modena, Italy. Luca Lombroso is greatly acknowledged for providing specific comments and feedback on these data. The research reported in the present paper was supported by Fondazione Cassa di Risparmio di Modena through the grant 2018-0093, by the University of Modena and Reggio Emilia through the grant FAR 2020 Mission Oriented, and by the European Union NextGenerationEU/NRRP, Mission 4 Component 2 Investment 1.5, Call 3277 (12/30/2021), Award 0001052 (06/23/2022), under the project ECS00000033 “Ecosystem for Sustainable Transition in Emilia-Romagna,” Spoke 6 “Ecological Transition Based on HPC and Data Technology.” The authors thank the anonymous reviewers for comments that led to improvement in the manuscript.

Funding

The authors have no relevant financial or non-financial interests to disclose.

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Author notes

  1. Stefano Orlandini

    Present address: Dipartimento di Ingegneria Enzo Ferrari, Università degli Studi di Modena e Reggio Emilia, Modena, Italy

  2. Sean Albertson

    Present address: College of Arts and Sciences, Cornell University, Ithaca, NY, USA

Authors and Affiliations

  1. Dipartimento di Comunicazione ed Economia, Università degli Studi di Modena e Reggio Emilia, Reggio Emilia, Italy

    Isabella Morlini

  2. Dipartimento di Ingegneria Enzo Ferrari, Università degli Studi di Modena e Reggio Emilia, Modena, Italy

    Sean Albertson

Authors
  1. Isabella Morlini
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Isabella Morlini, Sean Albertson and Stefano Orlandini. The first draft of the manuscript was written by Isabella Morlini and Stefano Orlandini and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Isabella Morlini.

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Appendix 1

Appendix 1

Considering annual values of the NAO teleconnection index, from 1950 to 2019, the statistical assessment of the presence or absence of a monotonic trend, inhomogeneity and change points, has been made by performing several nonparametric and parametric tests, using XLSTAT (Addinsoft 2023). P values of the different tests are reported in Table 6.

Table 6 P values of different homogeneity tests
Full size table

At the 1% level, all tests agree in accepting the null hypothesis that the annual values are independent, and the series is homogeneous. Correlations with the other climatic series of P and T are then likely to be nonspurious. Correlation coefficients and p values are reported in Table 7.

Table 7 Correlation coefficients and related p values (in brackets)
Full size table

The correlation between the NAO index and precipitation P, and the correlation between the NAO index and temperature T are clearly not significant. To further investigate the influence of the NAO index on the local temperature T and compare the nonlinear relationship between T and NAO with the nonlinear relationship between T and C and T and A, different smoothing splines and the 4-parameter logistic function are estimated. In Fig. 8, cubic smoothing splines with S = 1.0 and S = 0.2 and the 4-parameter logistic function LF are reported. Table 8 reports the NSE error (2) for smoothing splines. Clearly, smoothing splines with S = 1.0 overfit the data, while all the other estimated smoothing splines have similar AIC and BIC values (not reported) and can be selected as models with a proper degree of smoothness.

Fig. 8
figure 8

Time series of T and A (plot a), T and C (plot b), T and NAO (plot c), estimated values of T considering A (plot d) and C (plot e) and NAO (plot f) as dependent variable using smoothing splines (SS) with parameters 1.00 and 0.20 and the 4-parameter logistic function (LF)

Full size image
Table 8 NSE errors
Full size table

Both the graphical representation of the estimated functions and the values of the NSE indicate that local urbanization A and the global CO2 concentration C are more related to local temperature T than the NAO index and are better predictors of temperature changes in the last 70 years. In conclusion, results suggest that neither local precipitation P nor the NAO index seem to be related to the local temperature T. This may be because local geographical features may modify the impact of the NAO index on precipitation and temperature in specific areas.

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Morlini, I., Albertson, S. & Orlandini, S. Characterization of annual urban air temperature changes with special reference to the city of Modena: a comparison between regression models and a proposal for a new index to evaluate relationships between environmental variables. Stoch Environ Res Risk Assess 38, 1163–1178 (2024). https://doi.org/10.1007/s00477-023-02622-x

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