Surface and groundwater resource availability depends on precipitation patterns. Climatic change may alter not only future annual totals of precipitation but also its temporal distribution. In regions depending strongly on snow accumulation for steady water supply, this can lead to water constraints. We process climatic projections of precipitation from 19 models of the Climate Model Inter-comparison Project 5 for the Po river, Italy. The study area hosts Italy's most important lakes and reservoirs and is inhabited by 16 million people. The river basin is also known for its productive areas of irrigated agriculture. We apply a Bayesian processor of uncertainty, which we calibrate on a comprehensive set of high-resolution gridded observations. The processor outputs predictive densities of precipitation for selected prognostic time windows. These densities can be used in conjunction with an utility function to estimate potential losses and/or evaluate the benefits of mitigating actions. For the study area, annual precipitation will not change notably in the future for both an optimistic and a pessimistic scenario. The temporal distribution of precipitation will become affected. These potential changes result in considerable strain on storage capacity and water flows needed to satisfy irrigation demand as well as hydroelectric and thermal energy production.

  • We present a 21st-century precipitation and temperature climate analysis for Northern Italy using CMIP5 Scenarios RCP4.5 and RCP8.5.

  • The projections show a rather small change in seasonal precipitation totals.

  • The temperature increases considerably over the analysis period.

  • Snow depth and area extent will most likely decrease on average.

  • Italy will need to address future challenges in water resource management in the Po basin.

Graphical Abstract

Graphical Abstract
Graphical Abstract

Currently, we observe climatic changes that are linked to global warming caused by greenhouse gas emissions and are predicted to cause temperature and precipitation changes across many regions of the globe (IPCC 2021, 2022). While the land surface of continental masses may become warmer over the 21st century, precipitation patterns may also change, with some regions becoming, on average, drier and others wetter. Especially the frequency of extreme hydrometeorological events will change, with intense precipitation events becoming more numerous and drought increasingly extensive. Related natural hazards and risks may most likely increase.

The assessment of climate change-induced risks (Aven & Renn 2015) and the planning of mitigating actions (Strzepek et al. 2011) rely on multiple numerical integrations of Earth system models, which simulate, as realistically as possible, the interaction of atmosphere, land, ocean, and sea-ice processes. The physics in these models is described by a system of highly nonlinear governing equations, simulated on a three-dimensional grid with finite spatial resolution (IPCC 2013). Due to the chaotic nature of the Earth system (Lorenz 1963), the integration of the physical equations is affected by initial and boundary conditions, including pre-defined carbon emission scenarios (Palmer 2000). The solutions are, therefore, sensitive to model uncertainties, owing to the fact that real processes are simulated approximately and that the equations are resolved on a finite grid. As the forecast lead time increases, model uncertainties become dominant. Several multi-model ensemble simulations of future climate have been performed as part of the Climate Model Inter-comparison Project (CMIP), which to date include multiple executive phases (Meehl et al. 2000, 2007; Eyring et al. 2012; Taylor et al. 2012). Specialized studies on the Mediterranean region that were executed in the frame of the Coordinated Climate Experiment Project (CORDEX), a joint effort on downscaling CMIP5 (and more recently also CMIP6) projections to regional scales, point towards intensification of hydrometeorological extremes and considerable challenges ahead for the region (Pieri et al. 2017; Tramblay & Somot 2018).

The Po river valley is the largest single river basin in Italy and hosts the country's largest freshwater lakes. The densely populated basin area (225 inhabitants/km2) is also the largest contiguous and prolific agricultural area in Italy. It also hosts important service industries and manufacturing sites, including hydropower plants as well as thermal power stations sited along the river for cooling. Altogether, these activities are characterized by intense water use, whereby 87% of surface water use and 17% of groundwater use are attributable to irrigation alone. Economic activities in the Po basin contribute to 34% of the added value created in Italy (Musolino et al. 2018). The hydrology of the basin is dominated by liquid precipitation, which occurs mainly in autumn and spring, and snowpack accumulation in the high Alpine and Apennine ranges, which is ablated during spring, adding meltwater to river flows. Some four large natural lake systems at the foothills of the Alps are fed by runoff from alpine catchments and constitute large natural reservoirs, which have been artificially regulated during the first half of the 20th century. In conjunction with a series of much smaller artificial multi-purpose reservoirs in the Alps and the Apennines, they constitute important storage capacity for the regulation of surface water flows for the Po river and its tributaries, thus ensuring sufficient irrigation water supply during the dry season.

During the summer of 2022, the Po river experienced the largest drought of the last 70 years (Levantesi 2022), caused mainly by a lack of snow accumulation in the alpine part of the basin during the winter of 2021/2022 and the absence of liquid precipitation during several consecutive winter and spring months. At the beginning of August, the flow rate at the basin closing station Pontelagoscuro reached a low point of 100 m3/s, and far below the long-term minimum of 400 m3/s usually reached towards the end of the irrigation season. Simultaneously, warm air flows from the African continent across the Mediterranean-enhanced evaporation, putting ecosystems under particular water stress. If such types of extreme meteorological conditions become regular, it will cause severe water scarcity events that affect the entire socioeconomic and productive system in the basin. Besides the lack of water for consumption and irrigation, there are collateral effects like electric energy shortages due to reduced river flows for hydropower generation and cooling of thermal plants and saltwater intrusions from the Adriatic coast into the Po delta area, causing the salinization of fertile land. Mitigating actions would need to be devised, which require a credible prognosis of future precipitation and surface runoff, groundwater recharge, and temporal pattern of snowfall. To this end, we use climate projections from the Climate Model Inter-comparison Project Five (CMIP5), which need to be post-processed for bias correction and uncertainty quantification. While most studies agree on the future increase in temperature, results on local precipitation trends are conflicting, with some studies suggesting a considerable decrease in precipitation (Padulano et al. 2020), while others indicate no significant past and/or future trend (Ciccarelli et al. 2008; Braca et al. 2019).

Climate model projections are supposed to produce the general statistics of underlying climate variables (Knutti et al. 2010) but are likely to be biased in terms of mean and variance for the reasons mentioned previously. Hence, systematic post-processing of climate ensemble output is needed. Different techniques have been progressively proposed (Palmer & Räisänen 2002; Giorgi & Mearns 2003; Furrer et al. 2007; Rougier 2007; Tebaldi & Sansò 2009; Reggiani et al. 2021; Koutsoyiannis & Montanari 2022) and applied among others to variables of particular hydrological relevance, such as temperature and precipitation. However, most of these approaches assume that the spread of the ensemble projection is equal to the uncertainty of future climate.

The main objective of this work is to estimate the predictive density for precipitation in the Po valley in Italy. We perform a separate study on the precipitation of the river Po, in which we employ a large CMIP5 model output ensemble, which we elaborate through a Bayesian processor to correct on hand of past observations for bias of mean and variance and obtain the predictive distributions of future precipitation for the temporal windows 2035–2065 and 2070–2100. The predictive distribution is a conditional density that expresses the probability of future occurrences, given climate model projections that serve as pseudo-observations. The knowledge of the full predictive distribution of precipitation is an essential constituent for any decision-making process in undertaking mitigating actions (Reggiani et al. 2022). In this context, one must also address the issue of non-stationarity of the climate process. Non-stationarity can be addressed differently, either by assuming underlying linear or nonlinear trends (Buser et al. 2009), or, as done here, by assuming climate as a weakly stationary process, for which stationarity holds firm over the time windows of the preset length.

The proposed Bayesian processor was originally presented by Reggiani et al. (2021) and applied to temperature projections for the Po river basin. Here, we change the focus of that work by post-processing seasonal projections of precipitation. We first calibrate the processor by making use of comprehensive gridded datasets of precipitation, which have been generated by interpolating more than 50 years of rain gauge data from a dense observing network by the aggregation to seasonal totals. The calibrated processor yields bias-corrected estimates of seasonal precipitation and variance that are propagated by the climate models to the end of the 21st century. In this study, we choose two future climate scenarios, referred to as Representative Concentration Pathways (RCPs) by the IPCC (IPCC 2013), namely RCP4.5 as the more optimistic warming scenario and RCP8.5 as the pessimistic one.

The manuscript is structured into six sections. Section 2 introduces definitions and explains the methodology; Section 3 describes data and application; Section 4 presents the results; Section 5 discusses the water resource management implications in the Po river basin and Section 6 reports the conclusions. Supplementary Material is provided in Appendix A.

Predictive uncertainty

The predictive density is defined as the probability distribution of a quantity, conditional on all presently available information (Hamill & Whitaker 2006):
(1)
where is the vector of climatic observations (past or future) and is a vector of predictions of . These become the known quantities, which enhance our knowledge by conditioning the probability distribution of the observations . Future, not-yet observed, occurrences are indicated by , and their respective predictions by .

Climate projections are error-affected estimates of the future Earth system states serving as decisional knowledge support in reducing uncertainty through bias-removal and sharpening (Gneiting et al. 2007) of the probability density of conditional on . This conditional density is essential for decision-making in any downstream impact analysis.

Stochastic properties of climate projections

The principal difference between handling climate projections and classical short- and medium-range forecasts is that presently available projections may be capable of preserving the probability distributions of the simulated Earth system variables, but not their observed auto- and cross-correlation structure (Giorgi & Francisco 2000; Palmer 2000; Vidale et al. 2003; Déqué et al. 2007), a characteristic named asynchronicity (Stoner et al. 2013). For example, projections of precipitation are known to exhibit stronger autocorrelation than observed rainfall (Ines & Hansen 2006).

Conditioning of variates

Instead of conventional conditioning of a predictor on a predictand, we prefer ‘weakly’ conditioning the two variables similar to distribution matching (DM) (Wood et al. 2002; Drusch et al. 2005; Boé et al. 2007). This approach is used regularly for bias-correcting or downscaling Earth system model output or remotely sensed data against observations. DM (which we denote with instead of conventional conditioning indicated by ) is a form of conditioning, in which the mean does not depend on correlation, and hence, we call it weak conditioning. DM differs from quantile matching (QM), which uses empirical cumulative distribution functions (ECDFs) instead of fitted distribution models and can be advantageous for certain climatic variables (Themeßl et al. 2011). Both methods are also used for downscaling climate model output, a topic that is not of relevance here, where we deal with upscaling instead. When weakly conditioning two arbitrarily distributed variables, we apply probability matching between the ECDFs or by fitting appropriate parametric distributions F and G and by inverting one of the two (Hirsch 1982). In this way, one distribution morphs into the other. By setting the cumulative distribution function (CDF) of the observations equal to that of a predictor:
(2)
and then inverting :
(3)
We obtain a transformation T. This is equivalent to introducing a new variable with the same moments of the variate it is calibrated against. If the original variate is Gaussian, denoted with the Greek letter , T becomes:
(4)
with distribution:
(5)
The predictive density of the conditioned variable for the model j at time i is, hence, Gaussian:
(6)
with parameters:
(7)
where and are taken over all possible realizations of at time i. The predictive distribution of the projected variable conditional on model output is obtained in total analogy and it yields a series of probability distributions of the observations that are weakly conditional on each projection . For this distribution, the mean and variance derived from observations in Equation (7) are used because the bias with respect to observations and the variance of observations are assumed to hold also well into the future (Collins et al. 2006).

Weak conditioning through matching of Gaussian distributions has the advantage that one retains a parametric expression of type (6) over the entire distribution, including the tails, which allows one to better represent the predictive probability distribution for decision-making on adaptation measures (Reggiani et al. 2022).

Retrospective prediction and projections

As explained in Section 2.3., we use weak conditioning for retrospective predictions and projections. A prediction/projection is performed by estimating the density (1) at a time i. For a climate projection ensemble with multiple predictors, one can adopt the concept of mixture distribution, a weighted mean of univariate conditional distributions. For an arbitrarily (i.e. not necessarily Gaussian) distributed variate , the mixture distribution is :
(8)

The similarity sign indicates that the predictive distribution is ‘approximated’ by the mixture, while the hatted bold symbol indicates the -dimensional vector of predictions j at time i. Expressions for the mean and variance of the mixture distribution are given in Supplementary Material, Appendix A. The weights are the probability of the th ensemble member being a valid prediction. One can adopt two approaches in assessing the weights: (1) Bayesian Model Averaging (BMA) and (2) uniform weighting (UW), as shown in Reggiani et al. (2021).

BMA (Raftery et al. 2005) assumes non-uniform weights in (8) and maximizes the log-likelihood of observations:
(9)
Maximum likelihood estimation (MLE) of weights is a special case of maximum a posteriori (MAP) estimation that assumes a uniform prior distribution of the weights. An important assumption underlying BMA is the independence of variates. Some degree of dependency is inevitably present (Knutti et al. 2017) because the climate models of the CMIP5 ensemble use similar initial conditions. Nevertheless, because of the generally weak dependency between variates, we continue to assume full independence, as in classical BMA. The predictive mean and variance of the mixture distribution for the case of independent variates become (Supplementary Material, Appendix A):
(10)

For the present analysis, we simply assume exclusively UW when mixing the m univariate predictive densities , therefore giving no prior preference to any member of the climate model ensemble. The final expressions for the mixture can be derived from (8) by setting , with mean and variance given by (10). The described approaches, which require a transformation of variables into the Gaussian space, overcome the classical problem of hydrological statistical projections, which tend to be linear or nonlinear (Beven 2021), but hardly chaotic as required in a climate-changing environment. In the proposed approach, we use an ensemble of Earth system models to describe the chaotic projections into the future and the associated model projection uncertainty but subsequently use these projections as uncertain measures of future outcomes to finally assess the probability distribution of the actual future, albeit unknown, quantities.

Post-processing of precipitation projections is applied for the Po river basin as shown in Figure 1. A range of data pre-processing steps are necessary to prepare the datasets prior to climate output post-processing. The primary effort consists of projecting the CMIP5 output ensemble and observations onto a common regular spatial grid because the various CMIP5 models natively use different spatial resolutions and different grid projections.
Figure 1

The study area in the Po river basin in Italy and the common climate model grid for projections and observations. The cell numbering increases row-wise starting in the upper left corner, with analysis cells 3 and 9 framed in red and dots indicating cell centres. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.063.

Figure 1

The study area in the Po river basin in Italy and the common climate model grid for projections and observations. The cell numbering increases row-wise starting in the upper left corner, with analysis cells 3 and 9 framed in red and dots indicating cell centres. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/nh.2022.063.

Close modal

Observed precipitation

Our selected study region covers a rectangular area including the entire Po river basin in Northern Italy, as shown in Figure 1. The area extent is from in the N–W corner to in the S–E. The ground observations of precipitation, which are needed to calibrate the processor, consist of the Central-Northern Italy daily precipitation dataset ArCIS (Climatological Archive for Central-Northern Italy), a comprehensive gridded precipitation dataset ( km regular grid) covering the Italian territory above latitude . The product has been derived from 1,762 rain gauges that belong to different networks of 11 Italian administrative regions plus several stations in neighbouring countries. The temporal coverage extends over the 1965–2015 period at daily resolution (Pavan et al. 2019; Grazzini et al. 2020; ISPRA 2021). To make ArCIS congruent with the spatial resolution of CMIP5 climate output data, the original gridded data need to be upscaled by spatial averaging towards a spatial grid as shown in Figure 1. The averaging is performed using a ‘first-order conservative second-order conservative’ method (Jones 1999) included in the Climate Data Operator (CDO) software library (Schulzweida 2021). Finally, we aggregate the daily data series into seasonal totals. In summary, we obtain 15 series of seasonal precipitation totals that are representative of the cells in Figure 1 covering the basin area. The cell centres are indicated by blue dots.

Projected precipitation

As a next step, we process the outputs of the CMIP5 climate model ensemble. CMIP5 control simulations start on 01 January 1901 and end on 31 December 2005 and are made available as monthly means. The prognostic period reaches from 01 January 2006 through 31 December 2100. We select a 41 years’ baseline window (BW), 1965–2005; two 31 years’ prognostic windows, 2045–2065 (PW1) and 2070–2100 (PW2), and two RCP scenarios, RCP4.5 and RCP8.5, four cases in total. The monthly precipitation series from the 19 models listed in Table 1 are extracted from the global CMIP5 simulated precipitation output for the study area and aggregated to seasonal totals. The selected CMIP5 models' outputs have different spatial resolutions and need to be aligned by projection onto the selected common regular grid, in line with what has been done for observations, using once more the ‘first-order conservative second-order conservative’ mass-preserving interpolation technique (Jones 1999). At the end of processing, we obtain a series of seasonal data that are equally resolved in space and overlap temporally with the observation records for the 1965–2015 period.

Table 1

List of 19 global climate models from the CMIP5 experiment used as a climate projection ensemble over two prognostic windows in the 21st century

ModelSource organization
ACCESS1-0 Bureau of Meteorology – CSIRO AU 
BCC-CSM1-1 Beijing Climate Center, CN 
BCC-CSM1-1m moderate res.  
BNU-ESM Bejing National University, CN 
CanESM2 Canadian Centre Clim. Modelling and Analysis, CND 
CCSM4 Comm. Clim. Sys. Model V4, NCAR-UCAR, USA 
CESM1-CAM5 Comm. Earth Sys. ModelV1, Atmos. Sys. ModelV5, USA 
CNRM-CM5 Centre National Recherche Météorologique, FR 
CSIRO-Mk3-6-0 CSIRO AU 
GFDL-ESM2M Geophysical Fluid Dynamics Lab, USA 
GFDL-ESM2G  
INMCM4 Russian Academy of Sciences, RU 
IPSL-CM5A-MR Institut Pierre Simon Laplace, FR 
MIROC5 Model for Interdisciplinary Research on Climate, JP 
MIROC-ESM  
MIROC-ESM-CHEM  
MPI-ESM-MR Max Planck Institute, DE 
MRI-CGCM3 Meteorological Research Institute, JP 
NorESM1-M Norwegian Climate Center, NO 
ModelSource organization
ACCESS1-0 Bureau of Meteorology – CSIRO AU 
BCC-CSM1-1 Beijing Climate Center, CN 
BCC-CSM1-1m moderate res.  
BNU-ESM Bejing National University, CN 
CanESM2 Canadian Centre Clim. Modelling and Analysis, CND 
CCSM4 Comm. Clim. Sys. Model V4, NCAR-UCAR, USA 
CESM1-CAM5 Comm. Earth Sys. ModelV1, Atmos. Sys. ModelV5, USA 
CNRM-CM5 Centre National Recherche Météorologique, FR 
CSIRO-Mk3-6-0 CSIRO AU 
GFDL-ESM2M Geophysical Fluid Dynamics Lab, USA 
GFDL-ESM2G  
INMCM4 Russian Academy of Sciences, RU 
IPSL-CM5A-MR Institut Pierre Simon Laplace, FR 
MIROC5 Model for Interdisciplinary Research on Climate, JP 
MIROC-ESM  
MIROC-ESM-CHEM  
MPI-ESM-MR Max Planck Institute, DE 
MRI-CGCM3 Meteorological Research Institute, JP 
NorESM1-M Norwegian Climate Center, NO 

Normalization of distributions

Furthermore, we apply the processor by first comparing the distributions of the upscaled seasonal total observed precipitation for each of the 15 selected cells against those of the simulated seasonal climate for each member of the CMIP5 model ensemble. The predictive distribution (6) is formulated for Gaussian data. However, the distributions of observed and projected seasonal precipitation are mostly non-Gaussian, left-limited and need to be fitted with appropriate parametric models H. These are selected for each spatial cell and each temporal season among the log-normal, normal, gamma and Weibull distributions according to statistical hypothesis test outcomes. Figure 2 shows examples of parametric distributions H that were fitted to the 41 data points for selected cells and seasons.
Figure 2

Parametric distributions of 1965–2005 observed data for selected seasons and cells: (a) gamma; (b) log-normal; (c) normal; and (d) Weibull fits.

Figure 2

Parametric distributions of 1965–2005 observed data for selected seasons and cells: (a) gamma; (b) log-normal; (c) normal; and (d) Weibull fits.

Close modal
As a next step, the non-Gaussian variates , whose distributions are modelled as parametric distributions H, need to be mapped into standard Gaussian variates by normal quantile transform (NQT) through DM as in Equations (2) and (3):
(11)
where denotes the inverse standard normal distribution. Once observations and predictors have been transformed to standard normal variates, they can be conditioned as per Equations (4)–(7).

Post-processing

The actual post-processing phase starts by weakly conditioning the standard Gaussian series of the CMIP5 precipitation projection ensemble against those of standard normalized observations. To this end, we evaluate a univariate predictive distribution of type (6) for each of the j models, which is parameterized for each season through separate sets of values for the conditional mean and variance, as per (7). The stochastic relationship between the model and observations, therefore, depends on the mean and variance of observations and the Pearson correlation between standard normal observations and model projection.

Second, the univariate conditional distributions of daily data are weighted linearly as in Equation (8). The predictive Gaussian mean and variance for the BW are estimated via Equation (10). Finally, the fully Gaussian predictive distribution needs to be mapped back into the space of origin by inverse NQT:
(12)
where F and are, respectively, normal and the inverse standard normal distribution. We indicate the arbitrary zero-bound predictive distribution of the variate in the space of origin with and the density with . The latter corresponds to the predictive density of Equation (1). As is to be expected, it must assign zero probability to below-zero values of precipitation. The distribution has its own, non-necessarily Gaussian, mean and variance also given by (10). These PDFs can be traced either as a sample relative frequency histogram or approximated by a pdf estimated through a kernel density estimator, while mean and variance can be easily estimated from respective samples. Figure 3 visualizes the outlined post-processing steps by means of a flow chart.
Figure 3

A scheme of the variable transformation across the post-processing.

Figure 3

A scheme of the variable transformation across the post-processing.

Close modal
The post-processing results are presented for the four seasons of the year (December, January, February - DJF; March, April, May - MAM; June, July, August - JJA; September, October, November - SON) as the mean distribution for the season over the n years of the BW or the two predictive windows. The window-average distributions have a mean, which is equal to the mean of the predictive mean values , making up the window, the so-called mean of means . The window-mean variance is estimated in accordance with the law of total variance (Mahler & Dean 2001):
(13)
where and are, respectively, the expected value and variance taken over the n years of the window. The total variance (13) equals the mean of the predictive variances for the n individual years of the window plus the dispersion of the means around the mean of means. Figures 4 and 5 show the post-processed ensemble output for the two red-framed analysis cells 3 and 9 in Figure 1. For cell 3, we selected for cell RCP4.5, winter, and for cell 9 RCP8.5, spring. Both figures show the raw ensemble (pink) and the ensemble mean (purple). The bias-corrected predictive mean is indicated in bright red, whereas observations in the BW are represented in dark blue. The vertical dashed black lines indicate the limitations of the BW (left) and the two predictive windows PW1 (centre) and PW2 (right). The bold black dashed horizontal lines indicate the mean of means for the three windows. The grey shadowed areas show the predictive uncertainty through the 50 and 95% confidence intervals. One notices that post-processing removes the bias of the model ensemble with respect to observations and adjusts the predictive variance.
Figure 4

Cell 3, RCP4.5, winter (DJF) seasonal precipitation totals , unprocessed ensemble output , raw ensemble mean , predictive mean , UW. The shadowed areas indicate the 50–95% credible intervals.

Figure 4

Cell 3, RCP4.5, winter (DJF) seasonal precipitation totals , unprocessed ensemble output , raw ensemble mean , predictive mean , UW. The shadowed areas indicate the 50–95% credible intervals.

Close modal
Figure 5

Cell 9, RCP8.5, spring (MAM) seasonal precipitation totals , unprocessed ensemble output , raw ensemble mean , predictive mean , UW. The shadowed areas indicate the 50–95% confidence intervals.

Figure 5

Cell 9, RCP8.5, spring (MAM) seasonal precipitation totals , unprocessed ensemble output , raw ensemble mean , predictive mean , UW. The shadowed areas indicate the 50–95% confidence intervals.

Close modal

In the interest of decision-makers, we summarize the results concisely in terms of increments or decrements of total seasonal precipitation, which one can expect across the 21st century. To this end, we calculate the differences between the BW and, respectively, PW1 and PW2. Table 2 reports the percentual and absolute differences of the mean of means between BW and PW1 and between BW and PW2, respectively, for all seasons. Absolute values, expressed in mm, are given between parentheses.

Table 2

Percentual and absolute (mm) (in parenthesis) changes of precipitation between the mean of the baseline (BW) period and the mean of the two predictive windows PW1 and PW2, 4 seasons and 15 cells in Figure 1 

CellCoordinatesDJFMAMJJASONDJFMAMJJASON
PW1% (mm)PW2% (mm)
RCP4.5 
 − 0.56( − 2.0) 0.37(1.3) 0.65(1.88) − 0.85( − 2.9) 1.12(4.05) 0.17(0.62) − 1.5( − 4.31) 1.1(3.75) 
 − 0.25( − 0.56) 0.4(1.69) 0.61(2.2) − 0.71( − 3.3) 1.26(2.8) 0.5(2.08) − 1.45( − 5.29) 1.28(6.0) 
 − 0.71( − 1.54) 0.03(0.13) 0.98(4.65) − 1.1( − 5.37) 1.5(3.26) 0.52(2.193) − 1.28( − 6.08) 0.8(4.22) 
 − 1.1( − 1.81) − 0.13( − 0.39) 0.54(2.02) − 0.8( − 2.86) 2.6(4.36) 0.6(1.71) − 0.6( − 2.34) 0.93(3.3) 
 − 0.8( − 1.07) − 0.31( − 0.72) 0.53(1.6) 0.54(1.53) 3.07(4.14) 0.67(1.6) − 0.73( − 2.19) 1.0(2.9) 
 − 0.52( − 0.94) − 0.29( − 0.85) − 0.0( − 0.0) − 0.78( − 2.18) 1.51(2.74) − 0.1( − 0.25) − 0.76( − 1.8) 0.3 (0.93) 
 − 0.7( − 1.15) 0.23(0.7) 0.35(0.86) − 0.66( − 1.93) 1.5(2.26) 0.3(0.93) − 0.96( − 2.4) 0.63(1.84) 
 − 0.76( − 1.37) 0.5(1.27) 0.65(1.53) − 0.13( − 0.39) 1.44(2.58) − 0.23( − 0.58) − 1.12( − 2.65) 0.3(1.09) 
 − 0.89( − 1.5) 0.0(0.0) − 0.04( − 0.1) 0.42(1.2) 2.11(3.7) 0.2(0.46) − 0.6( − 1.6) 0.4(1.13) 
10  − 0.89( − 1.53) − 0.1( − 0.24) 0.42(1.04) 0.56(1.49) 2.47(4.26) − 0.19( − 0.4) − 1.0( − 2.53) 0.3(0.82) 
11  0.4(0.82) − 0.1( − 0.25) − 0.3( − 0.55) − 1.41( − 3.9) 0.43(0.77) − 0.4( − 1.21) − 0.95( − 1.93) 0.9(2.57) 
12  0.02(0.04) − 0.17( − 0.42) 0.49(0.71) − 1.14( − 3.25) 0.47(0.88) − 0.92( − 2.28) − 1.7( − 2.5) 1.26(3.58) 
13  − 0.3( − 0.97) 0.1(0.3) − 0.53( − 1.1) − 0.51( − 2.44) 0.21(0.6) − 0.65( − 2.0) − 0.7( − 1.4) 0.3(1.65) 
14  − 0.62( − 2.14) 0.31(0.97) − 0.9( − 1.96) − 0.9( − 4.47) 0.39(1.34) − 0.8( − 2.45) − 0.4( − 0.82) 0.8(3.47) 
15  − 0.99( − 2.45) − 0.04( − 0.11) − 0.5( − 0.9) − 0.77( − 2.5) 1.07(2.64) − 0.53( − 1.3) − 0.79( − 1.44) 0.35(1.15) 
RCP8.5 
 0.71(2.6) 0.91(3.26) 1.1(3.2) 0.94(3.2) 1.9(7.2) − 3.4( − 12.0) − 5.7( − 16.7) − 2.88( − 9.8) 
 0.67(1.5) 1.82(7.73) 0.9(3.4) 1.9(8.8) 3.3(7.3) − 4.7( − 20.3) − 6.4( − 23.41) − 4.6( − 21.7) 
 1.2(2.6) 1.7(7.15) 1.1(5.1) 1.37(6.75) 2.3(5.0) − 4.3( − 18.15) − 6.4 ( − 30.3) − 2.8( − 13.8) 
 1.6(2.6) 1.1(3.27) 0.97(3.6) 1.7(6.02) 2.0(3.3) − 4.1( − 12.06) − 5.0( − 18.6) − 2.86( − 10.15) 
 1.2(1.6) 1.17(2.8) 0.5(1.42) 1.6(4.5) 2.1(2.81) − 3.7( − 8.65) − 3.8( − 11.5) − 2.7( − 7.51) 
 1.6(2.9) 1.06(3.17) 1.25(2.95) 0.7(1.99) 1.72(3.12) − 4.7( − 14.05) − 6.62( − 15.5) − 4.5( − 12.5) 
 3.0(4.7) 1.72(5.27) 0.63(1.56) 0.9(2.63) 0.9(1.45) − 5.3( − 16.3) − 6.52( − 16.15) − 5.2( − 15.2) 
 2.3(4.14) 1.8(4.7) 1.37(3.2) 0.6(1.9) 0.8(1.4) − 5.1( − 13.0) − 6.99( − 16.53) − 3.3( − 9.9) 
 2.1(3.6) 1.18(2.75) 0.45(1.1) 1.4(4.11) 1.28(2.2) − 3.47( − 8.1) − 6.4( − 15.7) − 3.23( − 9.2) 
10  2.9(5.0) 1.46(3.32) 0.45(1.1) 0.97(2.6) 1.16(2.0) − 3.83( − 8.7) − 6.3( − 15.5) − 2.9( − 7.7) 
11  3.3(5.9) 2.12(6.16) 0.96(1.95) 1.0(2.9) − 2.1( − 3.73) − 5.9( − 17.14) − 9.9( − 20.2) − 5.9( − 16.4) 
12  3.7(6.95) 2.1(5.1) 0.3(0.4) 1.1(3.2) − 2.15( − 3.99) − 6.75( − 16.8) − 9.1( − 13.27) − 6.6( − 18.7)1 
13  2.1(6.7) 2.0(6.3) 0.9(1.84) 2.2(10.6) − 1.58( − 5.05) − 5.1( − 15.85) − 8.4( − 17.4) − 4.9( − 23.5) 
14  1.63(5.65) 1.41(4.44) 0.96(1.98) 2.0(9.1) − 1.44( − 4.99) − 4.61( − 14.5) − 7.97( − 16.5) − 4.21(18.9) 
15  1.43(3.54) 1.05(2.6) 0.98(1.8) 1.4(4.5) − 1.18( − 2.91) − 3.8( − 9.4) − 7.87( − 14.4) − 3.04( − 9.87) 
CellCoordinatesDJFMAMJJASONDJFMAMJJASON
PW1% (mm)PW2% (mm)
RCP4.5 
 − 0.56( − 2.0) 0.37(1.3) 0.65(1.88) − 0.85( − 2.9) 1.12(4.05) 0.17(0.62) − 1.5( − 4.31) 1.1(3.75) 
 − 0.25( − 0.56) 0.4(1.69) 0.61(2.2) − 0.71( − 3.3) 1.26(2.8) 0.5(2.08) − 1.45( − 5.29) 1.28(6.0) 
 − 0.71( − 1.54) 0.03(0.13) 0.98(4.65) − 1.1( − 5.37) 1.5(3.26) 0.52(2.193) − 1.28( − 6.08) 0.8(4.22) 
 − 1.1( − 1.81) − 0.13( − 0.39) 0.54(2.02) − 0.8( − 2.86) 2.6(4.36) 0.6(1.71) − 0.6( − 2.34) 0.93(3.3) 
 − 0.8( − 1.07) − 0.31( − 0.72) 0.53(1.6) 0.54(1.53) 3.07(4.14) 0.67(1.6) − 0.73( − 2.19) 1.0(2.9) 
 − 0.52( − 0.94) − 0.29( − 0.85) − 0.0( − 0.0) − 0.78( − 2.18) 1.51(2.74) − 0.1( − 0.25) − 0.76( − 1.8) 0.3 (0.93) 
 − 0.7( − 1.15) 0.23(0.7) 0.35(0.86) − 0.66( − 1.93) 1.5(2.26) 0.3(0.93) − 0.96( − 2.4) 0.63(1.84) 
 − 0.76( − 1.37) 0.5(1.27) 0.65(1.53) − 0.13( − 0.39) 1.44(2.58) − 0.23( − 0.58) − 1.12( − 2.65) 0.3(1.09) 
 − 0.89( − 1.5) 0.0(0.0) − 0.04( − 0.1) 0.42(1.2) 2.11(3.7) 0.2(0.46) − 0.6( − 1.6) 0.4(1.13) 
10  − 0.89( − 1.53) − 0.1( − 0.24) 0.42(1.04) 0.56(1.49) 2.47(4.26) − 0.19( − 0.4) − 1.0( − 2.53) 0.3(0.82) 
11  0.4(0.82) − 0.1( − 0.25) − 0.3( − 0.55) − 1.41( − 3.9) 0.43(0.77) − 0.4( − 1.21) − 0.95( − 1.93) 0.9(2.57) 
12  0.02(0.04) − 0.17( − 0.42) 0.49(0.71) − 1.14( − 3.25) 0.47(0.88) − 0.92( − 2.28) − 1.7( − 2.5) 1.26(3.58) 
13  − 0.3( − 0.97) 0.1(0.3) − 0.53( − 1.1) − 0.51( − 2.44) 0.21(0.6) − 0.65( − 2.0) − 0.7( − 1.4) 0.3(1.65) 
14  − 0.62( − 2.14) 0.31(0.97) − 0.9( − 1.96) − 0.9( − 4.47) 0.39(1.34) − 0.8( − 2.45) − 0.4( − 0.82) 0.8(3.47) 
15  − 0.99( − 2.45) − 0.04( − 0.11) − 0.5( − 0.9) − 0.77( − 2.5) 1.07(2.64) − 0.53( − 1.3) − 0.79( − 1.44) 0.35(1.15) 
RCP8.5 
 0.71(2.6) 0.91(3.26) 1.1(3.2) 0.94(3.2) 1.9(7.2) − 3.4( − 12.0) − 5.7( − 16.7) − 2.88( − 9.8) 
 0.67(1.5) 1.82(7.73) 0.9(3.4) 1.9(8.8) 3.3(7.3) − 4.7( − 20.3) − 6.4( − 23.41) − 4.6( − 21.7) 
 1.2(2.6) 1.7(7.15) 1.1(5.1) 1.37(6.75) 2.3(5.0) − 4.3( − 18.15) − 6.4 ( − 30.3) − 2.8( − 13.8) 
 1.6(2.6) 1.1(3.27) 0.97(3.6) 1.7(6.02) 2.0(3.3) − 4.1( − 12.06) − 5.0( − 18.6) − 2.86( − 10.15) 
 1.2(1.6) 1.17(2.8) 0.5(1.42) 1.6(4.5) 2.1(2.81) − 3.7( − 8.65) − 3.8( − 11.5) − 2.7( − 7.51) 
 1.6(2.9) 1.06(3.17) 1.25(2.95) 0.7(1.99) 1.72(3.12) − 4.7( − 14.05) − 6.62( − 15.5) − 4.5( − 12.5) 
 3.0(4.7) 1.72(5.27) 0.63(1.56) 0.9(2.63) 0.9(1.45) − 5.3( − 16.3) − 6.52( − 16.15) − 5.2( − 15.2) 
 2.3(4.14) 1.8(4.7) 1.37(3.2) 0.6(1.9) 0.8(1.4) − 5.1( − 13.0) − 6.99( − 16.53) − 3.3( − 9.9) 
 2.1(3.6) 1.18(2.75) 0.45(1.1) 1.4(4.11) 1.28(2.2) − 3.47( − 8.1) − 6.4( − 15.7) − 3.23( − 9.2) 
10  2.9(5.0) 1.46(3.32) 0.45(1.1) 0.97(2.6) 1.16(2.0) − 3.83( − 8.7) − 6.3( − 15.5) − 2.9( − 7.7) 
11  3.3(5.9) 2.12(6.16) 0.96(1.95) 1.0(2.9) − 2.1( − 3.73) − 5.9( − 17.14) − 9.9( − 20.2) − 5.9( − 16.4) 
12  3.7(6.95) 2.1(5.1) 0.3(0.4) 1.1(3.2) − 2.15( − 3.99) − 6.75( − 16.8) − 9.1( − 13.27) − 6.6( − 18.7)1 
13  2.1(6.7) 2.0(6.3) 0.9(1.84) 2.2(10.6) − 1.58( − 5.05) − 5.1( − 15.85) − 8.4( − 17.4) − 4.9( − 23.5) 
14  1.63(5.65) 1.41(4.44) 0.96(1.98) 2.0(9.1) − 1.44( − 4.99) − 4.61( − 14.5) − 7.97( − 16.5) − 4.21(18.9) 
15  1.43(3.54) 1.05(2.6) 0.98(1.8) 1.4(4.5) − 1.18( − 2.91) − 3.8( − 9.4) − 7.87( − 14.4) − 3.04( − 9.87) 

Due to the close geographical proximity of the chosen set of cells, the changes between cells are small. For the more optimistic RCP4.5 emission scenario, one recognizes a mostly neutral pattern in terms of precipitation change until the middle of the century and a slightly noticeable increase during winter and autumn, typically the wettest season, for the latter part of the century. For the more pessimistic RCP8.5 emission scenario, precipitation slightly increases with respect to the reference period until the middle of century across all seasons, while for the latter part of the century, it decreases across all seasons, with the exception of winter. From these results, we conclude that following CMIP5 climate simulations, seasonal total precipitation for both emission scenarios remains essentially stable over the Po valley. This result is congruent with the analysis of Braca et al. (2019), who also find no significant changes in total annual precipitation from their analysis of the NCAR Community Climate System Model (CCSM4) output (for reference, see Table 1) over Northern Italy as part of their climate analysis for the entire Italian peninsula and Campania region as a local target.

The near-stationarity of precipitation also justifies our choice of a 30-year analysis window for the application of the weakly stationary process assumption. Contrarily, the temperature for the study area changes more rapidly across the 21st century, a reason why predictive windows with a length of 20 years have to be chosen (Reggiani et al. 2021). Nevertheless, the climatic analysis of precipitation in a water resource management context needs to be analysed from a broader perspective, as addressed subsequently.

Despite projected seasonal precipitation totals not seeming to change significantly with respect to the ‘current’ 1965–2005 period, which we have selected as a control period, there are still implications for water resource management in the Po valley due to projected temperature changes across the 21st century.

Reggiani et al. (2021) analysed CMIP5 2-m temperature projections for the Po river basin. These were conditioned and corrected on the 1979–2005 ECMWF ERA5 temperature reanalysis (Hersbach et al. 2020) acting as observation proxy and then aggregated over the entire Po river basin area. Temperatures are altitude-corrected from the ERA5 grid cell elevation to a common reference height using the dry adiabatic lapse rate. In this precursory article to the present one, we performed a weighted combination of ensemble projections using UW as well as BMA weighting, with weights changing per month. Due to the evident non-stationarity of temperature, we had to shrink the predictive window length for PW1 and PW2 to 20 years, to reasonably apply the assumption of a weakly stationary process, instead of using 30-year windows as for precipitation. The analysis in Reggiani et al. (2021) clearly shows that spatial average temperature increments between the BW and the 2040–2060 (PW1) and 2080–2100 (PW2) predictive windows are considerable and, as to be expected, higher for the pessimistic RCP8.5 scenario. Table 3 summarizes the basin-average temperature changes as percentages and absolute values for all seasons, as reported in the paper.

Table 3

Percentual and absolute (°C) (in parenthesis) temperature changes between the mean of the baseline (BW) period and the mean of the 2 predictive windows PW1 and PW2, 4 seasons, Bayesian model averaging and uniform weighting

SeasonRCP4.5
RCP8.5
BWPW1PW2PW1PW2
T (°C)% (ΔT (°C))% (ΔT (°C))% (ΔT (°C))% (ΔT (°C))
Bayesian model averaging 
 DJF 0.24 458(1.1) 704 (1.7) 608 (1.46) 1,375(3.3) 
 MAM 8.79 18(1.6) 16.4(2.21) 16.3(2.1) 34(4.4) 
 JJA 18.73 13.3(2.50) 16.4(3.1) 16.4(3.1) 34.1(6.4) 
 SON 10.01 10.5(1.05) 24.3(2.4) 22.6(2.2) 46.2(4.6) 
Uniform weighting 
 DJF 0.24 530(1.2) 745(1.8) 720(1.73) 1,420(3.41) 
 MAM 8.79 17.3(1.5) 22(1.9) 21.7(1.91) 45(3.9) 
 JJA 18.73 11.1(2.1) 14.6(2.7) 15(2.80) 28.5(5.3) 
 SON 10.01 10(1.0) 22.1(2.2) 20.7(2.07) 44(4.39) 
SeasonRCP4.5
RCP8.5
BWPW1PW2PW1PW2
T (°C)% (ΔT (°C))% (ΔT (°C))% (ΔT (°C))% (ΔT (°C))
Bayesian model averaging 
 DJF 0.24 458(1.1) 704 (1.7) 608 (1.46) 1,375(3.3) 
 MAM 8.79 18(1.6) 16.4(2.21) 16.3(2.1) 34(4.4) 
 JJA 18.73 13.3(2.50) 16.4(3.1) 16.4(3.1) 34.1(6.4) 
 SON 10.01 10.5(1.05) 24.3(2.4) 22.6(2.2) 46.2(4.6) 
Uniform weighting 
 DJF 0.24 530(1.2) 745(1.8) 720(1.73) 1,420(3.41) 
 MAM 8.79 17.3(1.5) 22(1.9) 21.7(1.91) 45(3.9) 
 JJA 18.73 11.1(2.1) 14.6(2.7) 15(2.80) 28.5(5.3) 
 SON 10.01 10(1.0) 22.1(2.2) 20.7(2.07) 44(4.39) 

Source: Reproduced from Reggiani et al. (2021).

From the analysis of future precipitation performed here, in conjunction with the earlier study on future temperature, we can draw the following conclusions concerning climatic impacts on water resources in the Po river basin:

First of all, higher evapotranspiration, caused by higher temperatures, highly reduces the availability of renewable water resources for rain-fed agriculture in the Po valley, which in turn increases the need for artificial irrigation, if production is to be kept up. Moreover, the reduction of winter precipitation associated with higher temperatures, especially during winter and spring, pushes the climatic snow line to higher altitudes with lower amounts of precipitation stored as snowpack. As a result, the natural storage capacity of the snowpack is lost, with several consequences, such as the lack of slow recharge of water tables, which constitute a fundamental renewable water resource in the Po river basin, as well as the loss of water resource availability as surface runoff during the spring melting season. Finally, other observed aspects, which are not part of this study, are also worrisome, such as the reduction of the number of rainy days and the increase in precipitation intensity during storms, which enhances the fast transit of precipitated water towards the sea. Additional small and distributed surface storage capacity would be needed to increase the water availability, given the environmental implications and the lack of suitable low-risk sites. Therefore, even though the annual total precipitation may not change significantly, the availability of water resources will considerably drop, requiring water resource management strategies that are substantially different from those adopted at present. Adaptation strategies will also be required for the abatement of non-revenue water in potable water distribution systems by reducing distributed losses, which, in the Po valley, easily range from 20 to 40%. At the same time, crop types and irrigation practices in agriculture will have to be revisited in the light of preserving and optimizing the use of available water resources.

We would like to thank the Italian National Institute for Environmental Protection and Research (ISPRA) for making the gridded precipitation data for the Po river basin available. We also acknowledge the CMIP5 community for providing access to the climate output ensembles. This research was partly funded by Deutsche Forschungsgemeinschaft (DFG), Grant Number RE3848/4 awarded to the second author. We would like to thank three anonymous reviewers for their efforts, which have helped to improve the quality of the manuscript.

CMIP5 data can be downloaded from https://pcmdi.llnl.gov/mips/cmip5/. Gridded precipitation and temperature data for Northern Italy were downloaded from the site https://www.arcis.it.

The authors declare there is no conflict.

Beven
K.
2021
Issues in generating stochastic observables for hydrological models
.
Hydrological Processes
35
,
e14203
.
doi:10.1002/ hyp.14203
.
Boé
J.
,
Terray
L.
,
Habets
F.
&
Martin
E.
2007
Statistical and dynamical downscaling of the Seine basin climate for hydro-meteorological studies
.
International Journal of Climatology
27
,
1643
1655
.
doi:10.1002/joc.1602
.
Braca
G.
,
Bussettini
M.
,
Ducci
D.
,
Lastoria
B.
&
Mariani
S.
2019
Evaluation of national and regional groundwater resources under climate change scenarios using a GIS-based water budget procedure
.
Rendiconti Lincei. Scienze Fisiche e Naturali
30
,
109
123
.
doi:10.1007/ s12210-018-00757-6
.
Buser
C. M.
,
Künsch
H. R.
,
Lüthi
D.
,
Wild
M.
&
Schär
C.
2009
Bayesian multi-model projection of climate: bias assumptions and interannual variability
.
Climate Dynamics
33
,
849
868
.
doi:10.1007/ s00382-009-0588-6
.
Ciccarelli
N.
,
von Hardenberg
J.
,
Provenzale
A.
,
Ronchi
C.
,
Vargiu
A.
&
Pelosini
R.
2008
Climate variability in north-western Italy during the second half of the 20th century
.
Global and Planetary Change
63
,
185
195
.
doi:10.1016/j.gloplacha.2008.03.006
.
Collins
M.
,
Booth
B. B. B.
,
Harris
G. R.
,
Murphy
J. M.
,
Sexton
D. M. H.
&
Webb
M. J.
2006
Towards quantifying uncertainty in transient climate change
.
Climate Dynamics
27
,
127
147
.
doi:10.1007/s00382-006-0121-0
.
Déqué
M.
,
Rowell
D. P.
,
Lüthi
D.
,
Giorgi
F.
,
Christensen
J. H.
,
Rockel
B.
,
Jacob
D.
,
Kjellström
E.
,
de Castro
M.
&
van den Hurk
B.
2007
An intercomparison of regional climate simulations for Europe: assessing uncertainties in model projections
.
Climatic Change
81
,
53
70
.
doi:10.1007/ s10584-006-9228-x
.
Drusch
M.
,
Wood
E. F.
&
Gao
H.
2005
Observation operators for the direct assimilation of TRMM microwave imager retrieved soil moisture
.
Geophysical Research Letters
32
.
doi:10.1029/2005GL023623
.
Eyring
V.
,
Bony
S.
,
Meehl
G. A.
,
Senior
C. A.
,
Stevens
B.
,
Stouffer
R. J.
&
Taylor
K. E.
2012
Overview of the coupled model intercomparison project phase 6 (CMIP6) experimental design and organization
.
Geoscientific Model Development
9
,
1937
2016
.
Furrer
R.
,
Knutti
R.
,
Sain
S.
,
Nychka
D.
&
Meehl
G. A.
2007
Spatial patterns of probabilistic temperature change projections from a multivariate Bayesian analysis of climate model output
.
Geophysical Research Letters
34
.
doi:10.1029/2006GL027754
.
Giorgi
F.
&
Mearns
L. O.
2003
Probability of regional climate change calculated using the reliability ensemble average (REA) method
.
Geophysical Research Letters
30
,
1629
1632
.
doi:10.1029/2003GL017130
.
Gneiting
T.
,
Balabdaoui
F.
&
Raftery
A. E.
2007
Probabilistic forecasts, calibration and sharpness
.
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
69
,
243
268
.
doi:10.1111/j.1467-9868.2007.00587.x
.
Grazzini
F.
,
Craig
G. C.
,
Keil
C.
,
Antolini
G.
&
Pavan
V.
2020
Extreme precipitation events over northern Italy. Part I: a systematic classification with machine-learning techniques
.
Quarterly Journal of the Royal Meteorological Society
146
,
69
85
.
doi:https://doi.org/10.1002/qj.3635
.
Hersbach
H.
,
Bell
B.
&
Berrisford
P. E. A.
2020
The ERA5 global reanalysis
.
Quarterly Journal of the Royal Meteorological Society
.
doi:10.1002/qj.3803
.
Hirsch
R. M.
1982
A comparison of four streamflow record extension techniques
.
Water Resources Research
18
,
1081
1088
.
Ines
A. V. M.
&
Hansen
J. W.
2006
Bias correction of daily GCM rainfall for crop simulation studies
.
Agricultural and Forest Meteorology
138
,
44
53
.
IPCC
2013
Climate change 2013: the physical science basis
. In:
Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change
.
Cambridge University Press
,
Cambridge
,
UK;
New York, NY, USA
.
doi:10.1017/CBO9781107415324
.
IPCC
2021
Climate change 2021: summary for policymakers
. In:
Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change
.
Cambridge University Press
,
Cambridge
,
UK
;
New York, NY, USA
.
doi:10.1017/9781009157896.001
.
IPCC
2022
Climate change 2022: impacts, adaptation and vulnerability
. In:
Contribution of Working Group II to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change
.
Cambridge University Press
,
Cambridge
,
UK
;
New York, NY, USA
.
doi:10.1017/9781009325844.001
.
Available from
: www.climatechange2013.org.
ISPRA
2021
Il Bilancio Idrologico GIS-Based a Scala Nazionale su Griglia Regolare – BIGBANG. Technical Report 339
.
Istituto Superiore per la Protezione e la Ricerca Ambientale
.
Jones
P. W.
1999
First- and second-order conservative remapping schemes for grids in spherical coordinates
.
Monthly Weather Review
127
,
2204
2210
.
doi:10.1175/1520-0493(1999)127 < 2204:FASOCR > 2.0.CO;2
.
Knutti
R.
,
Furrer
R.
,
Tebaldi
C.
,
Cermak
J.
&
Meehl
G. A.
2010
Challenges in combining projections from multiple climate models
.
Journal of Climate
23
,
2739
2758
.
doi:10.1175/2009JCLI3361.1
.
Knutti
R.
,
Sedláček
J.
,
Sanderson
B. M.
,
Lorenz
R.
,
Fischer
E. M.
&
Eyring
V.
2017
A climate model projection weighting scheme accounting for performance and interdependence
.
Geophysical Research Letters
44
,
1909
1918
.
doi:10.1002/2016GL072012
.
Koutsoyiannis
D.
&
Montanari
A.
2022
Climate extrapolations in hydrology: the expanded BlueCat methodology
.
Hydrology
9
.
doi:10.3390/hydrology9050086
.
Levantesi
S.
2022
. Italy Must Prepare for A Future of Chronic Drought
.
Springer Nature
,
Italy
.
doi:10.1038/d43978-022-00089-y
.
Lorenz
E. N.
1963
Deterministic non-periodic flow
.
Journal of the Atmospheric Sciences
20
,
130
141
.
Mahler
H. C.
&
Dean
C. G.
2001
Chapter 8: credibility
. In:
Foundations of Casualty Actuarial Science
, 4th edn.
Casualty Actuarial Society
,
Arlington, VA
, pp.
525
526
.
Meehl
G. A.
,
Boer
G. J.
,
Covey
C.
,
Latif
M.
&
Stouffer
R. J.
2000
The coupled model intercomparison project (CMIP)
.
Bulletin of the American Meteorological Society
81
,
313
318
.
Meehl
G. A.
,
Covey
C.
,
Delworth
T.
,
Latif
M.
,
McAvaney
B.
,
Mitchell
J. F. B.
,
Stouffer
R. J.
&
Taylor
K. E.
2007
The WCRP CMIP3 multimodel dataset: a new era in climate change research
.
Bulletin of the American Meteorological Society
88
,
1383
1394
.
Musolino
D.
,
Vezzani
C.
&
Massarutto
A.
2018
Chapter 3.11
. In:
Drought Management in the Po River Basin, Italy
.
John Wiley & Sons, Ltd
, pp.
201
215
.
doi:10.1002/9781119017073.ch11
.
Padulano
R.
,
Lama
G. F. C.
,
Rianna
G.
,
Santini
M.
,
Mancini
M.
&
Stojiljkovic
M.
2020
Future rainfall scenarios for the assessment of water availability in Italy
. In:
2020 IEEE International Workshop on Metrology for Agriculture and Forestry (MetroAgriFor)
, 4–6 November 2020.
IEEE
, New York. pp.
241
246
. doi:10.1109/MetroAgriFor50201.2020.9277599.
Palmer
T. N.
2000
Predicting uncertainty in forecasts of weather and climate
.
Technical Reports on Progress in Physics
63
.
Palmer
T. N.
&
Räisänen
J.
2002
Quantifying the risk of extreme seasonal precipitation events in a changing climate
.
Nature
415
,
512
514
.
doi:10.1038/415512a
.
Pavan
V.
,
Antolini
G.
,
Barbiero
R.
,
Berni
N.
,
Brunier
F.
,
Cacciamani
C.
&
Cagnati
A.
2019
High resolution climate precipitation analysis for north-central Italy, 1961–2015
.
Climate Dynamics
52
,
3435
3453
.
doi:10.1007/ s00382-018-4337-6
.
Pieri
L.
,
Rondini
D.
&
Ventura
F.
2017
Changes in the rainfall – streamflow regimes related to climate change in a small catchment in northern Italy
.
Theoretical and Applied Climatology
129
,
1075
1087
.
Raftery
A. E.
,
Gneiting
T.
,
Balabdaoui
F.
&
Polakowski
M.
2005
Using Bayesian model averaging to calibrate forecast ensembles
.
Monthly Weather Review
133
,
1155
1174
.
Reggiani
P.
,
Todini
E.
,
Boyko
O.
&
Buizza
R.
2021
Assessing uncertainty for decision-making in climate adaptation and risk mitigation
.
International Journal of Climatology
41
,
2891
2912
.
Reggiani
P.
,
Talbi
A.
&
Todini
E.
2022
Towards informed water resources planning and management
.
Hydrology
9
(
8
),
1
18
.
doi:10.3390/hydrology9080136
.
Rougier
J.
2007
Probabilistic inference for future climate using an ensemble of climate model evaluations
.
Climatic Change
81
,
247
264
.
doi:10.1007/s10584-006-9156-9
.
Schulzweida
U.
2021
CDO User Guide. Technical Report
.
Max Planck Institute
.
doi:10.5281/zenodo.5614769
.
Stoner
A. M. K.
,
Hayhoe
K.
,
Yang
X.
&
Wuebbles
D. J.
2013
An asynchronous regional regression model for statistical downscaling of daily climate variables
.
International Journal of Climatology
33
,
2473
2494
.
doi:10.1002/joc.3603
.
Strzepek
K.
,
McCluskey
A.
,
Boehlert
B.
,
Jacobsen
M.
&
Fant
C.
IV
2011
Climate Variability and Change: A Basin Scale Indicator Approach to Understanding the Risk to Water Resources Development and Management. Technical Report
.
The World Bank
,
Washington, DC
,
USA
.
Taylor
K. E.
,
Stouffer
R. J.
&
Meehl
G. A.
2012
Summary of the CMIP5 experiment design
.
Bulletin of the American Meteorological Society
93
,
485
498
.
Themeßl
M. J.
,
Gobiet
A.
&
Leuprecht
A.
2011
Empirical-statistical downscaling and error correction of daily precipitation from regional climate models
.
International Journal of Climatology
31
,
1530
1544
.
doi:10.1002/joc.2168
.
Tramblay
Y.
&
Somot
S.
2018
Future evolution of extreme precipitation in the Mediterranean
.
Climatic Change
151
,
289
302
.
doi:10.1023/B:CLIM.0000044622.42657.d4
.
Vidale
P. L.
,
Lüthi
D.
,
Frei
C.
,
Seneviratne
S. I.
&
Schär
C.
2003
Predictability and uncertainty in a regional climate model
.
Journal of Geophysical Research: Atmospheres
108
.
doi:10.1029/2002JD002810
.
Wood
A. W.
,
Maurer
E. P.
,
Kumar
A.
&
Lettenmaier
D. P.
2002
Long-range experimental hydrologic forecasting for the eastern United States
.
Journal of Geophysical Research
107
,
1
13
.
doi:10.1029/2001JD000659
.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY-NC-ND 4.0), which permits copying and redistribution for non-commercial purposes with no derivatives, provided the original work is properly cited (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Supplementary data