1 Introduction

Urbanization is an unavoidable and important aspect of human progress and is bound to increase with each passing day. However, while urbanization may be considered as an advantage to boost the economy, infrastructure, and life standards, climate change hazards like floods, heatwaves, etc. could be a major threat to the sustainability of urban development. (R.K. Pachauri & Meyer, 2014) As suggested by (Naison D. Mutizwa-Mangiza; Ben C. Arimah; Inge Jensen; Edlam Abera Yemeru; Michael K. Kinyanjui., 2011) both urbanization and climate change are co-evolving in such a way that densely packed populations in urban areas are being placed at much higher risk in the coming future. Understanding the interrelation between urbanization and local climate, though complex, is the need of the hour and the focus of this study.

Cities are the centre of human activities like production, transportation, energy consumption at residential and industrial zones hence major contributors in emission of greenhouse gases. Based on data from remote sensing, a study found that the 100 urban areas with the most carbon emissions are responsible for 18% of the world's carbon footprint.In 98 countries, the top three urban areas account for more than one-quarter of national emissions. (Moran et al., 2018).

According to (Mohan et al., 2011; Revi et al., 2015), one of the major concerns for urban infrastructure managers in India over the last few decades has been changes in the intensity and frequency of precipitation leading to extreme events. Precipitation frequency and intensity changes are not independent and somewhere, local physical processes play a very significant role in their change. (Mondal & Mujumdar, 2015).

Some of the recent studies (Golroudbary et al., 2019; Niyogi et al., 2017) suggest that urbanization is one of the presently leading parameter which effects in climate change resulting in modification of precipitation patterns.

The mechanisms of increased precipitation have been observed on the downwind of urban landscapes. (Huff & Changnon, 1972) It has been observed by (Kishtawal et al., 2010) that the increasing trend in the frequency of heavy precipitation events over the Indian monsoon region is almost at the same pace as over the regions where the trend of land use/land cover change through urbanization is fastest. (Shastri et al., 2015) also observed that the urban signatures on extreme precipitation are not prominently and consistently visible, but they are spatially non uniform.

Local temperature changes significantly impact intensity and frequency of extreme precipitation. (Mondal & Mujumdar, 2015) where intensity of extreme precipitation events increases with increase in temperature (Sharma & Mujumdar, 2019) and is also found to be the best influence for short duration Precipitation (Agilan & Umamahesh, 2017).

The Clausius-Clapeyron (CC) scaling relationship is widely used to obtain the relationship between precipitation and temperature. (Busuioc et al., 2017; Herath et al., 2018; G. Lenderink et al., 2017). (Westra et al., 2014) suggested that the effect of temperature on extreme precipitation can’t be separated easily from the combined effect of atmospheric variables. Therefore, correct interpretation of scaling can only be done by an understanding of atmospheric variables and physical processes. For this study, non-stationary extreme value modelling is used to find the impacts of physical drivers on extreme precipitation.

20% of urban dwellers worldwide live in 417 medium-sized cities with 1 million to 5 million inhabitants. Altogether, a total of 446 medium-sized cities are expected to be home to almost one-fourth of the urban population of developing countries in 2030 (UN, 2015). Hence, a successful sustainable urban planning agenda will require attention to be given to urban settlements of all sizes. The study of urban observations can provide a scientific research foundation for sustainable planning by broadening information to include different types of cities located in different climates (Mills, 2009). Urban designers and planners must adopt a comprehensive vision of urban climate science as a guiding principle to steer urban development strategy (Ye & Niyogi, 2022).

This study aims to investigate precipitation intensity variation in a growing urbanization city and its influential factors. Vadodara city is one of the smaller and growing cities in India, which makes it an ideal candidate to investigate the precipitation variations from average intensity to maximum precipitation intensity.

This study result indicates that growing cities can experience mean and heavy precipitation due to local temperature variation, but a one-day annual extreme precipitation event happens due to a combination of global and local physical drivers.

2 Study area

Vadodara, the third-largest city of Gujarat state, has a prominent place in the western part of India since the times of Gaekwar rulers, (1880). Located on Mumbai Ahmedabad industrial corridor, Vadodara faced rapid change after 1970 due to industrial growth, particularly in the petrochemical, textile and pharmaceutical sectors. Vadodara lies on the golden quadrilateral transportation network connecting major cities of India with a tremendous scope of development.

Authors residing in Vadodara since more than 30 years have witnessed growth of the city as well as change in climate, identified the area covered under the administrative boundaries of Vadodara Municipal Corporation for the purpose of the present study.

The area situated at an altitude 35.5 m above mean sea level having relatively flat terrain with the ground sloping from northeast to southwest in a mild manner. The topography broadly follows the basin of Vishwamitri river which flows through the heart of the city. It is situated between the latitude of 22.2° to 22.5° and a longitude of 73.1° to 73.3° grid box. Figure 1 shows the location of Vadodara.

Fig. 1
figure 1

Location of Vadodara

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The climate of Vadodara city is characterized as hot and semi-arid, with an average annual precipitation of 806 mm. The average annual rainy days are 37. The average annual maximum temperature is 34.4 °C, and the average annual minimum temperature is 21.3 °C (IMD, 2021).

The urbanization pattern of Vadodara can be traced through its population growth pattern. The population of Vadodara was below 0.21 million till 1950 (Fig. 2). The effect of industrial growth can be seen on the population rise. A steep upswing can be observed in the population after 1970. The population of Vadodara city is 1.67 million as per the 2011 census. The area under the Vadodara Municipal boundary is around 159 square kilometres in the year 2019.

Fig. 2
figure 2

Census of Vadodara

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As per the report of McKinsey Global Institute (Sankhe et al., 2010), Vadodara will have a population of 4.2 million and an expected GDP of 35 billion dollars by 2030. Study of the impact of global and local factors on precipitation of Vadodara can be analogued to other faster-growing tier-2 cities in India. Unlike megacities, there is a wider scope of implementation of climate resilience policies in such cities.

3 Data

Local daily precipitation, local daily temperature, global temperature, ENSO and satellite imageries were collected and processed for the study period 1970–2017 to find the impact of local and global factors on local annual and extreme precipitation of the study area. The study period was selected due to (a) the major urbanization of Vadodara started after 1970 (b) continuous data availability for the study period.

3.1 Precipitation and temperature data

Daily precipitation data and daily temperature data of the urban Vadodara weather station situated at longitude 73º 16′ 00" E and latitude: 22º 20′ 00" N were obtained from the India Meteorological Department (IMD) for the duration of 1970–2017.

3.2 Anomalies as a Covariate data

Local and global temperature data, ENSO and satellite imagery data collected from various agencies were not used directly. Anomalies of the processed data have been used as covariates to analyze changes in urbanization extremes.

3.2.1 Urban temperature anomalies (AMTA & SMTA)

Aerosols and surface properties in urban climate have a large influence on near-surface air temperature at the micro and local scale (Wang et al., 2018). With two criteria, local mean temperature anomalies were developed to see how precipitation behaves with variations in pre-monsoon (summer) and annual mean temperature. The Annual Mean Temperature Anomaly (AMTA) was developed for the whole year, i.e. from January to December, and the Summer Mean Temperature Anomaly (SMTA) for the summer months, i.e., from March to June, using the respective average temperature of the base period 1970–1999.

3.2.2 Urbanization anomalies (UGRA)

Landsat satellite images were used to detect the change in land use and land cover (LULC) of Vadodara between 1973 and 2018. (Table 1) The result unequivocally demonstrates the growth of urban area over the period of the study.

Table 1 Details of satellite data
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Satellite images were processed using GIS software. All the available land use land cover was categorized and selected to perform Maximum Likelihood Classification. The output was in the form of supervised classification for different years, and calculations were made to find out the particular land cover pattern. The achieved results were verified with ground reality. Land use and land cover for different years (Fig. 3a-i) indicate that urban expansion geared up after 1988.

Fig. 3
figure 3

Landuse landcove maps (a) 1973 (b) 1977 (c) 1981 (d) 1988 (e) 1993 (f) 1998 (g) 2003 (h) 2008 (i) 2013 (j) 2018

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Trends for different LULC like urban, vegetation, water bodies, and barren land can be seen in Fig. 4. The growth of the urban area of Vadodara can be better represented with an exponential trend. The extracted urban area is used for urban growth modelled by the exponential function as described by Eq. 1.

$$y=2\times {10}^{-35}{e}^{0.0419x}$$
(1)
Fig. 4
figure 4

Landuse landcover change for Vadodara (1973–2018)

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Here \(y\) is urban land in a square kilometre and \(x\) is the corresponding year.

The urban expansion area for each year from 1970–2017 was calculated from the above formula. Since urbanization follows an exponential function, the modelled value of urban area can't be used directly. Instead, it must be converted to natural logarithm. Urban Growth Rate Anomalies (UGRA) are calculated by taking the mean value of the natural logarithm of the base period 1970–1999, used as a covariate for this study.

3.2.3 Global surface temperature anomalies (GTA)

Studies (Allan & Soden, 2008; O’Gorman, 2015) show global warming is a primary indicator of climate change with rising temperatures and precipitation intensification on regional and global scales. Global warming is also attributed to human-induced climate change, the growth of major cities, and the industrial revolution (Trenberth, 2011).

The Surface Temperature Analysis (GISTEMP v4) of the NASA Goddard Institute for Space Studies (GISS) is an estimation of the global change in surface temperature (Hansen et al., 2010). The Global Surface Air Temperature Anomaly (GTA) series with respect to the 1951–1980 mean is used as a global warming indicator.

3.2.4 ENSO anomalies (AMEI)

The El-Niño Southern Oscillation (ENSO) is the most important phenomenon of the global climate that has the potential to alter the global circulation of the atmosphere. Sir Gilbert Walker (Kripalani & Kulkarni, 1997) first suggested that there was a relationship between the precipitation of the Indian monsoon and the ENSO. Many studies (Kripalani & Kulkarni, 1997; Ummenhofer et al., 2011) show the global impact of ENSO at a regional level by establishing the relationship between Indian summer monsoon precipitation and ENSO on the inter-decade time scale.

ENSO can be tracked by the Multivariate ENSO Index (MEI), which is determined from the six observed variables such as sea level pressure, zonal and meridional components of the surface wind, sea surface temperature, surface air temperature, and total cloudiness fraction of the sky over the tropical Pacific.

The MEI, which we used to get more details about the coupled ocean–atmosphere phenomenon, was introduced by (Wolter & Timlin, 1998). In the present analysis, we use the MEI average from November to March, i.e., AMEI as the data covariate.

4 Methodology

The IPCC Special Report on Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation (Field et al., 2012) refines the concept by stating that "an extreme (climate) event is generally defined as the occurrence of a weather or climate variable above (or below) the threshold value near the upper (or lower) ends of the range of variables observed."

As a preliminary investigation, extreme precipitation and temperature trends of Vadodara have been detected. The effect of maximum daily temperature on extreme precipitation was analyzed with binning and the Clausius-Clapeyron relationship. The non-stationary nature of the hydrological process can vary depending on a variety of reasons for urban cities. The influence of anomalies of physical drivers on extreme precipitation can be modelled and scaled with the GEV distribution. The schematic flow chart shown in Fig. 5 summaries the flow of the methodology.

Fig. 5
figure 5

Methodology

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4.1 Extreme precipitation and maximum temperature trend

The Expert Team on Climate Change Detection and Indices (ETCCDI) has developed a set of descriptive extreme indices. (Alexander et al., 2006; Frich et al., 2002; Zhang et al., 2011). All ETCCDI indices were calculated for each year and fitted with linear regression. F-test was used to verify the statistical significance of the linear regression.

One-day annual extreme Precipitation and temperature time series trend and change point were calculated using the non-parametric trend test Mann–Kendall (MK) and Pettit test. These tests are well known for the detection of monotonic trends in (Sheng Yue et al., 2002) hydrological series.

4.2 Binning method for scaling precipitation and daily maximum temperature

(Hardwick Jones et al., 2010) concluded that the availability of moisture at higher temperatures is extremely important. Consequently, the unavailability of a sufficient amount of moisture at higher temperatures leads to a decrease in scale and relative humidity. Precipitation-temperature scaling phenomena by the Binnig method approach studied by (Geert Lenderink & Van Meijgaard, 2008). Modification of the Binning Process has been suggested by (Herath et al., 2018; Wasko & Sharma, 2015).

Temperature data was sorted and combined with precipitation ≥ 0.1 mm. The temperature bins were allocated an equivalent number of pairs per bin (Hardwick Jones et al., 2010) and the median temperature value of each bin was used to classify the bin. Different percentile precipitation intensities are determined for each bin. The regression equation was fitted to the logarithmic values of precipitation of the 50th, 90th, and 99th percentiles.

(Herath et al., 2018) also highlighted in their study that the precipitation-temperature scaling relationship varies with the time window and a C–C (Clausius-Clapeyron) relationship can be established between daily/sub-daily extreme precipitation and maximum temperature.

The relationship between precipitation (P) and temperature is described by Eq. 2 (Utsumi et al., 2011).

$${P}_{2}={P}_{1}{\left(1+\alpha \right)}^{\Delta T}$$
(2)

where, \({P}_{1}\) and \({P}_{2}\) are the precipitation percentile at temperature \({T}_{1}\) and \({T}_{2}\) respectively. \(\alpha\) becomes the precipitation-temperature scaling coefficient. Where, \(\alpha =6.8\mathrm{\% }{\mathrm{^\circ{\rm C} }}^{-1}\) at \(25\mathrm{^\circ{\rm C} }\) equivalent to Clausius-Clapeyron.

Precipitation and daily maximum temperature data for Vadodara are divided into four 12-year windows (1970–1981, 1982–1993, 1994–2005, and 2006–2017). For each window, precipitation-temperature pairs are classified into 20 bins. 50, 90, and 99 percentile precipitation are estimated for each bin.

Linear regression is fitted in two regimes for each window by finding the slope for the first ten bins and another 10 bins. This helps to find out the slope for different percentiles of precipitation on the minimum daily maximum temperature range and the maximum daily maximum temperature range.

4.3 The generalized extreme value distribution

The GEV distribution function is defined as \(G\left(x\right)=exp\left[-{{\left\{1+\xi \left(\frac{x-\mu }{\sigma }\right)\right\}}_{+}}^{-\frac{1}{\xi }}\right]\) Where \(\sigma >0\) and \(-\infty <\mu ,\xi <\infty\). Three types of GEV distribution functions exist i.e. Gumbel, Fréchet and (reverse) Weibull distributions with three parameters: location, scale \(\sigma\) and shape \(\xi\) parameter. If \(\xi =0\) it represents Gumbel distribution, \(\xi >0\) it represents Fréchet distribution and \(\xi <0\) it represents Weibull distribution as described in Eq. 3 (Coles, 2004).

$$G\left(x;\mu ,\sigma ,\xi \right)=exp\left[-{{\left\{1+\xi \left(\frac{x-\mu }{\sigma }\right)\right\}}_{+}}^{-\frac{1}{\xi }}\right] \xi <0$$
(3)
$$\left[-exp\,exp \left(\frac{x-\mu }{\sigma }\right) \right] \xi =0$$
$$1+\xi \left[\frac{x-\mu }{\sigma }\right] \xi >0$$

Non-stationary processes have characteristics that change systematically through time. It is often apparent because of seasonal effects, perhaps due to different climate patterns in different months, or in the form of trends, possibly due to long-term climate changes. Non-stationarity only in location, scale parameter, and shape parameter cannot be estimated very precisely and assuming it as a smooth function of time is unrealistic (Coles, 2004). Therefore it has been considered as a constant. In this study, three cases have been assumed:

A stationary case, where model parameter was assumed to be constant.

A non-stationarity case where the location parameter assumed through covariates which is given by Eq. 4

$$\mu \left(t\right)={\mu }_{0}+{\mu }_{1}*covariate$$
(4)

A non-stationarity case where the location and scale parameter assumed through covariates which can be shown by Eq. 5 and 6 respectively.

$$\mu \left(t\right)={\mu }_{0}+{\mu }_{1}*covariate(t)$$
(5)
$$ln\sigma \left(t\right)={\sigma }_{0}+{\sigma }_{1}*covariate(t)$$
(6)

This study helps us to investigate the effect of urban local (AMTA, SMTA, UGRA) and global (GTA, AMEI) anomalies as a covariate on one-day extreme annual precipitation.

4.4 Selection criteria between models

The best non-stationary model choice is based on the Likelihood-Ratio test and information criteria. (Mondal & Mujumdar, 2015). The Likelihood-Ratio test compares two nested models in which the base model is a stationary model and the base model with more parameters is a non-stationary model. Suppose \({l}_{0}\) is the log-likelihood value for the stationary model and \({l}_{1}\) for non-stationary model. Then the test statistic, called the deviance statistic as shown in Eq. 7.

$$D=2\left({l}_{1}-{l}_{0}\right)$$
(7)

follows an approximate \({\chi }_{v}^{2}\) distribution function with a degree of freedom \(v\), equal to the difference in the number of parameters between the two models. The null hypothesis that \(D=0\) is rejected if \(D\) exceeds the \(1-\alpha\) quantile of the \({\chi }_{v}^{2}\) distribution function.

Akaike Information Criterion (AIC) can be defined as shown in Eq. 8.

$$AIC\left(p\right)=2{n}_{p}-2l,$$
(8)

where \({n}_{p}\) is the number of parameters in the \(p\)-th model, and \(l\) is maximized log-likelihood value. Among the non-stationarity models, the lower AIC value from stationary models is preferred.

4.5 Graphical visualization for selected models

Graphical Visualization confirms that our fitted models have appropriate quality. QQ and PP plots are used for model diagnostics. Due to the lack of homogeneity in the distributional assumptions for each observation, some modification is needed in non-stationary cases. Therefore, the data was transformed into a standard Gumbel distribution (residual) and applied for quality of the fitted non-stationary model. (Coles, 2004; Sharma & Mujumdar, 2019).

5 Results and discussion

5.1 Precipitation and temperature changes

All ETCCDI indices (Alexander et al., 2006) have been evaluated for each year with fitted linear regression, and the F-test is used to verify the statistical significance of linear regression. The Tn10p amount of cold nights following decreasing trend where Tn90p amount of warm night follows increasing trend as shown in Fig. 6(a-b) Similarly, TX10p, amount of cool day follows growing trend where TXGT50P, the fraction of days with above average temperatures are following increasing trend shown in Fig. 6(c-d). The results of temperature indices indicate a significant change in the temperature of Vadodara city.

Fig. 6
figure 6

Variations in temperature indices (a) Tn10P (Amount of cold nights), (b) TN90P (Amount of Warm nights), (c) TX10P (Amount of Cool days), (d) TXgt50P (Fraction of days with above average temperature)

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The precipitation index SDII daily precipitation intensity which is the ratio of annual precipitation to the number of wet days follows increasing trend shown in Fig. 7(a). As shown in Fig. 7(b-c), the linear fit of total annual precipitation from heavy rainy days R95p and very heavy rainy days R99p follows an increasing trend. PRCPTOT (annual total wet-days precipitation) follows a significant linearly increasing trend for the entire study period, as shown in Fig. 7(d). Maximum 1-day and 5-day annual Precipitation shown in Fig. 7(e–f) which are liable for flood events also follow increasing trend. It is important to examine whether the rising trends of daily extreme precipitation and temperature are associated with a rise in urbanization.

Fig. 7
figure 7

Variation in precipitation indices (a) SDII (density index), (b) R95P (Total annual PR from heavy rain days), (c) R99P (Total annual PR from very heavy rain days), (d) PRCPTOT (Annual total wet-day precipitation), (e) Rx1day (Maximum 1-day annual precipitaion)

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5.2 Effect of urban area on maximum temperature & precipitation

Maximum one-day annual precipitation and annual average temperature with urban expansion on the natural log axis is plotted in Fig. 8. It is evident that the annual average temperature is rising with urban expansion. The rise in the magnitude of maximum one-day annual precipitation also follows the rise in urban area and annual average temperature. The analysis gives preliminary confirmation of the effect of urbanization on therise of one day maximum precipitation.

Fig. 8
figure 8

Effect of urban area on average annual temperature and one-day maximum precipitation

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5.3 Scaling relationship between precipitation and daily maximum temperature

Clausius-Clapeyron scaling with the binning method is used to establish a relationship between precipitation and daily maximum temperature as described in section-4.2. Linear regression is used for developing scaling relation between daily maximum temperature and precipitation.

Figure 9(a–d) depicts the scale variations for the 50th, 90th, and 99th percentiles with two linear regimes over four different time spans (1970–1981, 1982–1993, 1994–2005, and 2006–2017)

Fig. 9
figure 9

Scale variations on 4 different time periods for Vadodara city (a) 1970–1981, (b) 1982–1993, (c) 1994–2005 and (d) 2006–2017 for 50th, 90th and 99th percentile with two linear regimes

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Scale variation of temperature is specifically observed from one time slice, revealing that daily maximum temperature varies from 27.15 to 36.9 degrees Celsius from 1970 to 1981; from 27.9 to 37.2 degrees Celsius from 1982 to 1993; from 27.6–38.6 degrees Celsius from 1994 to 2005; and from 27.5 to 38.4 degrees Celsius from 2006 to 2017. An increase of 1 to 2 degrees Celsius can be observed between 1970 and 2017. The maximum temperature range is further bifurcated into high and low regimes.

The 50th percentile of precipitation on high maximum temperature regime shows a decreasing trend ranging from -1.90% to -7.03% per degree Celsius during the whole study period. While on the low maximum temperature regime, it shows a comparatively more steep decreasing trend, which ranges from -10.17% (1982–1993) to -14.18% (1994–2005) per degree Celsius.

The steepness of the trend slope of the 90th percentile precipitation per degree Celsius over the study period becomes milder. For the high maximum temperature regime, it shows (Fig. 9a, b, and c) the values -1.87, -2.02 and -0.50% for the first three time intervals respectively. The positive (increasing) trend with the value 2.72% was observed for the last interval (2006–2017). Even though increasing trend has observed on high maximum temperature regime in the last interval, the decreasing trend with the value -8.41% on low maximum temperature regime can be observed in Fig. 9(d). The analysis shows the extreme precipitation increases with the temperature rise.

The intensity of 99th percentile precipitation increased by 1.22% between 1982 and 1993 (Fig. 9-b) and by 2.94% between 2006 and 2017 (Fig. 9-d) for the high daily maximum temperature regime. A 99th percentile precipitation event is one of the infrequent extreme events that can happen due to many physical and climatic factors. These factors can be found by non-stationarity modelling for one-day annual maximum precipitation.

5.4 Non-stationarity modelling for precipitation

The above discussion indicates that there is a major correlation between precipitation variation and temperature change. Mann-Kendal, Sens slope and Pettit’s test applied on average annual precipitation and local mean temperature of Vadodara city. The Mann-Kendal sign trend test for precipitation indicates an increasing trend at a 95% confidence level, with Sens slope estimator indicating a trend rate of 1.3395 mm/year and Pettit's test indicating a decreasing shift in the central tendency of time series with a change point in 1996, as shown in Fig. 10(a). Similarly, at a 95% confidence level, local mean temperature is increasing at a rate of 0.02 degree Celsius/year, with a shift in the central tendency of time-series changes at the year 2000 shown in Fig. 10(b).

Fig. 10
figure 10

Change points for Vadodara city (a) Average precipitation 1970–2017 (b) Average temperature 1970–2017

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Non-stationarity GEV model with linear trend in location and log-transformed scale parameter developed by anomalies of five physical drivers namely summer local temperature (SMTA), annual local temperature (AMTA), urbanization (UGRA), global average temperature (GTA) and ENSO cycle (MEI) and their possible combinations, 1 stationary and 21 non-stationary models are constructed by using 2 cases which are discussed in Sect. 4.1. Table 2 provides details of both the stationary and non-stationary models for one-day extreme annual precipitation. Models fitted with covariate values were evaluated on the basis of minimum AIC and minimum LR-test p-value in order to achieve the best fit. Models performing well are shown with bold letters.

Table 2 Generalised extreme value models
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After model fitting following points are observed:

If a model with a single covariate is taken into account, Model 4, having global average temperature anomalies as a covariate with a location parameter, performed the best of all 22 models with an AIC value of 519.47 and a Likelihood Ratio of 0.008. It indicates that global temperature anomalies have the greatest impact on local precipitation of Vadodara.

The second best of the other models is model 6 having AIC and LR values as 519.627 and 0.009 respectively, with urbanization anomalies as a location parameter covariate. It confirms that the maximum one-day rainfall is influenced by urbanization, even in medium-sized cities such as Vadodara.

Summer local temperature anomalies also play one of the major role in non-stationary extreme modelling, which can be seen as a combined effect with global average temperature on location and urbanization on scale by model 17, with an AIC value of 519.35 and LR value of 0.011. It might be due to the fact that summer surface air temperature variations are linked to inter seasonal variation of the Indian monsoon precipitation, which controls the land-climate coupling by modulating the soil moisture variations. Model 17 thus also confirms the effect of local temperature on maximum daily precipitation along with global temperature and urbanization.

Apart from the three models mentioned above, the other best models from stationary are also a combination of global average temperature, urbanization, summer and annual local mean temperature anomalies. Global average temperature and urbanization anomalies are playing a major role in local temperature anomalies as the individual model with this covariate does not show a significant relationship with one-day annual extreme precipitation.

In order to ensure that the best 3 models are actually a good representation of the data, QQ-PP plots were generated. QQ-PP plots were prepared for the shortlisted three models to compare stationary and non-stationary scenarios. It was observed that non-stationarity QQ-PP plots confirm the capture of quantiles for extreme precipitation intensities adequately. Figure 11(a-d) and Fig. 12(a-d) show the QQ and PP plots for stationary as well as non-stationary scenarios for the four models.

Fig. 11
figure 11

The QQ plot for stationary (a) M1 and best fitted non-stationary GEV model (b) M4 (c) M6 (d) M17

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Fig. 12
figure 12

PP plot for stationary (a) M1 and best fitted non-stationary GEV model (b) M4 (c) M6 (d) M17

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6 Summary and conclusion

This study reveals the association of precipitation with temperature on mean, heavy, and extremely heavy precipitation. A non-stationarity extreme value model is used with different covariates to find the physical factors that influence one-day annual extreme precipitation.

The results of the indices indicate that precipitation and temperature are varying due to urbanization as warmer nights rise, whereas days above average temperature and summer days also rise. Equivalently, total annual precipitation from heavy to very heavy rainy days also rises with one-day maximum to five-day maximum annual precipitation. The result shows that temperature variations are possibly an influential factor for precipitation.

A Clausius-Clapeyron relationship is developed between the range of daily maximum temperature and precipitation for finding precipitation intensity which is influenced by the increase in maximum temperature. Urbanization is one of the crucial factors that led to an increase in the daily maximum temperature and the creation of urban heat island. Different time-slice windows show that as urbanization increases, the daily maximum temperature is also rising by 1–2 degrees Celsius, which leads to a decrease in the 50th percentile precipitation and an increase in the 90th percentile precipitation at the high range of daily maximum temperature. Whereas 99th percentile precipitation results do not show a very significant relationship with maximum temperature regimes, that leads us toward non-Stationarity extreme value modelling.

Non-stationary extreme value modelling results indicate that the local mean temperature is not the only essential physical factor that influences one-day annual extreme precipitation for medium-sized cities. Global average temperature and urbanization are playing a major role along with the local mean temperature at the current size of the city. As it grows towards metro city, local mean temperature becomes more influential. Considering individually, urbanization is definitely an important physical driver influencing the one-day annual extreme precipitation value. The combined effect of urbanization and local temperature covariates has a significant influence on the precipitation extremes. It is important, however, to understand and zero down on the most influential parameter affecting precipitation extremes. So, while temperature is the major parameter influencing precipitation globally or regionally, it is the rate of urbanization that triggers the change in the local temperature, thus leading to extreme events of precipitation locally.

The study reveals that the average annual precipitation is decreasing but extreme precipitation is increasing with higher temperatures that may lead to a severe water crisis. The Ajwa reservoir, situated upstream of Vadodara, is one of the major sources of water supply to the city. On the other hand, spillway release from Ajwa into the river Vishwamitri causes flooding in many parts of the city. The rise in extreme precipitation will impact inter-annual operations of reservoir and optimization between safety and storage for water supply.

It is found that the urban per capita water demand is higher and municipal water supply is insufficient. Hence, groundwater is becoming a major source for domestic water needs. Precipitation is the sole source of groundwater recharge. The rise of extreme precipitation results in the generation of higher runoff and a lesser time of concentration. Recharging groundwater in this situation would be more difficult, and there would be more deterioration in groundwater quality and a drastic drop in groundwater tables in urban areas.

Considering the fact that ground water contributes to more than 50% of the urban water supply for domestic purposes, the combination of reduced groundwater recharge and insufficient storage of surface water would be critical to rising water demand.

Vadodara is one of India’s 100 smart cities. Under the Smart Cities mission, the government of India is investing heavily in the cities with the objectives of planning mixed land use, technology-driven smart solutions for citizen services, infrastructure development, and disaster management.

The present analysis of the physical drivers of climate change in the urban area is posing a serious threat to the socio-economic development and objectives of the smart cities mission. Criteria for feasibility assessment and designing for river fronts, pond rehabilitation, rainwater harvesting, groundwater recharging, land use planning, and flood mitigation in a changing climate for holistic development can be updated in the light of such studies. The present study can be used as a base and it can be extended to other growing or smart cities.