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Official Journal of the Asia Oceania Geosciences Society (AOGS)

Benchmark analysis of forecasted seasonal temperature over different climatic areas


From a long-term perspective, an improvement of seasonal forecasting, which is often exclusively based on climatology, could provide a new capability for the management of energy resources in a time scale of just a few months. This paper regards a benchmark analysis in relation to long-term temperature forecasts over Italy in the year 2010, comparing the eni-kassandra meteo forecast (e-kmf®) model, the Climate Forecast System–National Centers for Environmental Prediction (CFS-NCEP) model, and the climatological reference (based on 25-year data) with observations. Statistical indexes are used to understand the reliability of the prediction of 2-m monthly air temperatures with a perspective of 12 weeks ahead. The results show how the best performance is achieved by the e-kmf® system which improves the reliability for long-term forecasts compared to climatology and the CFS-NCEP model. By using the reliable high-performance forecast system, it is possible to optimize the natural gas portfolio and management operations, thereby obtaining a competitive advantage in the European energy market.


The advent of computer technology has led scientists to developing complex models to forecast natural gas consumption by improving calculation algorithms and using different statistical methods (Smith et al. 1996; Gorucu and Gumrah 2004; Sánchez-Úbeda and Berzosa 2007; Forouzanfar et al. 2010; Soldo 2012). An efficient management of energy distribution system often requires outlook prediction in relation to energy demand (Mirasgedis et al. 2006; Potocnik et al. 2007; Dovrtel and Medved 2011; Oldewurtel et al. 2012; Petersen and Bundgaard 2014), which is strictly related to seasonal weather and climatic trends. Therefore, meteorological information must be primarily seen to have potential positive impacts on the socio-economic areas of society (Leviäkangas and Hautala 2009).

Energy companies use this connection between meteorological variability and energy demand to provide effective scheduling in order to be protected against market variability during the most critical periods. For this reason, they are one of the most active users of seasonal climate forecasts, using these products in their long-term planning. The prediction of the natural gas is affected by residential, commercial, industrial and thermoelectric demands. The balance between offer and demand minimizes the risk of a sudden price increase. A weather forecast can also optimize processes in combined heat and power (CHP) plants and contribute to reducing costs concerning imbalance charges on the national power grid. Therefore, the possibility of obtaining meteorological trends (i.e. temperature, pressure, humidity) in advance in a given combined-cycle gas turbine (CCGT) power plant is useful to obtain competitive prices on the electricity market, and reduced errors in temperature forecasts allow a reduction in penalties for exceeding the power capacity that can be generated on the electricity market in which the company operates.

By knowing the temperature forecast for a certain geographical area in advance, and paying particular attention to anomalous trends, it is possible to improve the planning of storage reserves, as well as sales and supplies of natural gas. An exceptionally warm winter, for example, can leave energy companies with excess fuel reserves or, on the contrary, a colder winter creates the necessity of purchasing reserves at higher prices. Although the price changes in relation to the demand, some price adjustments do not compensate possible losses deriving from anomalous weather and climatic conditions; these are also crucial aspects according to climate change scenarios (Vidrih and Medved 2008; Franco and Sanstad 2008; Isaac and van Vuuren 2009; Zhou et al. 2014).

The degree day value is generally used as a measure to indicate the demand for energy to heat or cool buildings. Assuming a direct relationship between the volume of natural gas demand and the heating degree day (HDD) in the winter season in Italy, a hypothetical variation of 2°C with respect to climatology could cause:

  1. (i)

    an increase in commercial and residential demand of about 20%;

  2. (ii)

    an increase in industrial demand of about 8%;

  3. (iii)

    no increase in the demand for electricity for utilities for an overall variation of 10–15% with respect to the overall energy demand.

Consequently, operational activities and flexibility on the natural gas market could be improved for arbitrage opportunities (infra-month activities-unused capacity) of trading framework. Similarly, assuming a direct relationship between the volume of natural gas demand related to power generation by Electrical Utilities and the cooling degree day (CDD) in the summer season, a variation in the overall energy demand of about 7% can be estimated with a variation of 1°C with respect to climatological values (Giorgetti et al. 2012). Hence, the primary benefit of weather forecasting in the energy services is an advance warning for better energy distribution and management. For instance, a reliable weather forecast for a few days ahead is important for production from renewable sources, especially in the wind power generation where meteorological forecasts are widely used (Alexiadis et al. 1998; Pinson et al. 2009; Cassola and Burlando 2012; Carvalho et al. 2014).

Even if many atmospheric forecast improvements have been carried out in the last 20 years, it is important to bear in mind what Lorenz, the father of the chaos theory, stated in 1963: “It is impossible for long term forecasts, those made with a range of 2 weeks or more, to predict the state of the atmosphere with certainty, owing to the chaotic nature of the fluid dynamics equations involved” (Cox 2002). Therefore, in relation to season timescales, one of the most difficult areas of forecasting, the perennial question as to whether it will be cold or warm in a given region has been a major challenge (Palmer and Hagedorn 2006). Customers would certainty like easier decision-making, but this is normally impossible due to the effect of the above-mentioned chaos theory and processes we cannot resolve. Hence, in order to predict with any certainty, a good starting point is climatology, which provides the best available guidance to a customer when no other predictive elements are available. Historical data provide the frequency of an event, but, since climatology is static and representative of an average over a period of time, it is not capable of forecasting variations using these averages. Therefore, a good forecasting system can be defined as one that is superior to climatology (Palmer and Hagedorn 2006).

In relation to the above-mentioned issues, this paper shows the results of an innovative proprietary meteorological model for seasonal term temperature forecasting (from 1 to 12 weeks), developed by eni S.p.A in collaboration with the Epson Meteo Centre, mainly to predict the demand for energy and improve the management of natural gas stocks, their purchase and sale in different regions of Europe, i.e. Italy (north, centre and south), Belgium, Germany (north and centre-south), and France (north and south) (Giunta and Salerno 2013).

In particular, the proposed study includes a benchmark analysis for long-term temperature forecasts in Italy in the year 2010, comparing two meteorological models:

  1. (i)

    the eni-kassandra meteo forecast (e-kmf®);

  2. (ii)

    the CFS-NCEP (Climate Forecast System–National Centers for Environmental Prediction) model developed by the National Atmospheric and Oceanographic Administration (NOAA).

The metrics for temperature forecast evaluation include standard skill scores commonly used in scientific literature (Wilks 2006; Jolliffe and Stephenson 2003; WWRP-WGNE Joint Working Group on Verification 2015) to assess the reliability of air temperature forecasts at 2 m for a lead time of 12 weeks in three geographical areas in Italy (north, centre and south). The statistical analysis has been computed for the two models and for the climatological mean (the reference period is 1984–2008) in comparison with the observed data for each month of the year 2010. The results show how the best performance is achieved by the e-kmf® model in comparison with the CFS-NCEP model which, especially for northern Italy, shows a significant underestimation of temperatures. The use of the e-kmf® model, instead of the common climatological reference, may improve the long-term forecasting reliability by 35% as computed in the data analysis for the year 2010. This forecasting tool provides an alternative solution to statistical systems based on historical values.

The forecasting models and observed temperature database

In this section, the Italian area where the performance of 2 m-air temperature forecasts of the two models have been verified against climatology and observed data is described. A short description of the models and the characteristics of weather stations whose temperature data have been considered both for climatology and for the year 2010 daily observations are also provided.

The area of study

The area of study is the Italian peninsula divided into three sub-regions (macro-areas), north, centre and south (Figure 1), in order to reflect the main climate variations over the country together with the differences in energy demand. In fact, most of the north of Italy shows a humid continental climate due to the presence of the Po Valley, while a Mediterranean climate can be assigned to the central and southern Italy, as well as the coastal area of the north of the country. Moreover, the presence of the Alps and the Apennines, two important mountain chains, also plays a main role in the Italian climate. Finally, the Po Valley is the most populated and industrialized area with high energy consumptions, while central and southern Italy are less populated and show a lower energy demand.

Figure 1
figure 1

Grid points of the two climate models for the three areas of Italy (north, centre and south) represented by green rectangles; the e-kmf® model grid is shown with orange dots while the CFS-NCEP model grid with blue dots; geographical location of Italian weather stations (68 in total) below 500 m a.s.l. used for observed data of the year 2010 and for computing the climatological mean (1984–2008) in the three reference areas are shown with red dots. The horizontal grid point for both models are on a regular latitude–longitude grid spaced by 1°.

The Kassandra Meteo forecast model

The e-kmf® global forecast system uses a multi-model and ensemble technique (Goddard et al. 2001; Mason et al. 1999) to develop the meteorological prediction of temperature from the short-medium term (typically 1–10 days) to the long-term (~2–12 weeks) forecasts (Reichler and Roads 2004). Short and medium-term forecasts are provided by using regional and limited-area models with a grid size ranging from 5.5 km to 18 km, while long-term forecasts, as in this case study, are produced using two global models with 20 perturbed initial conditions (plus one control member) each, in order to obtain a multi-model with 40 ensemble forecasts.

The first global model has a horizontal spectral triangular truncation of 126 waves (T126) and 42 sigma pressure hybrid layers (L42), while the second one is a global modified version of the WRF-ARW (weather research and forecasting–advanced research WRF) model using 42 vertical levels and a horizontal grid of about 90 km. The final output of the whole ensemble is on a regular latitude-longitude grid spaced by 1°, as shown in Figure 1, with a temporal output every 6 h and a forecast horizon of 90 days. Initial conditions are derived from the global forecasting system (GFS) initial condition model which comes from the gridpoint statistical interpolation (GSI) global data assimilation system (GDAS) and it incorporates a 3D-Var (Three Dimensional–Variational Data Assimilation) method to continuously update the background fields used for the initial condition. The model uses global sea surface temperature (SST) boundary conditions (Reichler and Roads 2003) based on the SST anomaly simulated by a mixed-layer model. For each ensemble simulation, both the models make use of different physical and dynamical schemes for micro-physics (Lim and Hong 2010; Hong et al. 2004), Planetary Boundary Layer and Surface Layer (Hong et al. 2006, 2008; Bretherton and Park 2009; Pleim 2006, 2007; Beljaars 1994), cumulus parameterization (Kain 2004; Han and Pan 2011), radiation (Iacono et al. 2008; Dudhia 1989; Mlawer et al. 1997), and land surface physics (Niu et al. 2011; Yang et al. 2011; Noilan and Planton 1989; Pleim and Xiu 1995).

Finally, to obtain a single value to compare with observed and climatological data in the proposed benchmark, a selection procedure of the ensembles is applied to these two models. This selection process is applied for each time period defining a measure based on the distance between each member and the best member ensemble which is determined by using several normalized model variables; this measure is used for excluding all values outside of a defined range. The overall final value is computed by a weighted average of the remaining members.

The CFS-NCEP model

The CFS-NCEP Climate Forecast System (Saha et al. 2014) was designed and executed as a global, high-resolution, coupled atmosphere–ocean–land surface-sea ice system. The CFS data was developed by NOAA’s National Centres for Environmental Prediction (NCEP). The data for this study are freely accessible in GRIB2 (Gridded Binary) format from NOAA’s National Operational Model Archive and Distribution System (NOMADS) which is stored at NOAA’s National Climatic Data Centre (NCDC).

The atmospheric model has a horizontal spectral triangular truncation of 126 waves (T126, equivalent to nearly a 100 km grid resolution, which is directly comparable to the resolution of e-kmf® global models), a finite differencing vertically with 64 sigma pressure hybrid layers, a time resolution of 6 h and a forecast horizon of 4 months which can be compared with the e-kmf forecast which has a similar overlapping period of 12 weeks as lead time. The Noah land surface model (Ek et al. 2003) is employed in the CFS in both the coupled land–atmosphere–ocean model to provide land-surface prediction of surface fluxes (surface boundary conditions), and in the global land data assimilation system (GLDAS) to provide the land surface analysis and evolving land states. For further details about this model please refer to Saha et al. (2010).

Observations and climatology

The basic temperature observation data used for both the comparison with models and the climate history regard Italian weather stations and are taken from SYNOP (surface SYNOPtic observations) and METAR (METeorological Aerodrome Report). In this study 68 weather certified stations below 500 m above sea level have been taken into account (Figure 1; Table 1). Temperatures are collected on an hourly and daily basis and stored in data base to produce all the observed data. For a long-term comparison between forecasts and observations, temperature data have been aggregated into weekly mean values for each reference area (north, centre and south of Italy, considering only the continental areas without the two main islands). The same weekly mean values have been used both for comparing observed and forecasted data and for arranging the climatology for each reference area. A 25-year reference period for climate data has been considered (1984–2008). For each week of the year, a mean temperature value (based on 25-year data) has been obtained and used as the climatological reference for a comparison with observations and forecasts.

Table 1 Italian weather stations below 500 m a.s.l. used for observed data of the year 2010 and for the climatological mean (1984–2008)

The benchmark analysis

Temperature forecasts produced by the two models (e-kmf® and CFS-NCEP) have been compared on the basis of statistical indexes that allow the evaluation of the performance of the two models. The aim of this study is to quantify how temperature forecasts from meteorological models and climatological behavior perform in respect to the observed data for the three Italian macro-areas at different forecast time horizons. For both models, the forecasted data are the air temperatures at 2 m above the ground on a regular latitude-longitude grid spaced by one degree (Figure 1) with a time interval of 6 h to be compared with the observed and climatological data. The benchmark analysis is performed on the forecasted data at weekly time resolution and at three macro-area spatial resolution with a forecasted horizon of 12 weeks according to the following equations that provide the macro-area weekly forecast:

$$\overline{T}^{i}_{j,k,d} = \frac{1}{4}\sum\limits_{i = 1}^{4} {T_{j,i,d,k} }$$
$$\overline{{\overline{T}^{i} }}^{k}_{j,d} = \frac{1}{5}\sum\limits_{k = 1}^{5} {\overline{T}^{i}_{d,j,k} }$$
$$Tw_{j} = \frac{1}{7}\sum\limits_{d = 1}^{7} {\overline{{\overline{T}^{i} }}^{k}_{j,d} }$$
$$Ta = \frac{1}{N}\sum\limits_{j = 1}^{N} {Tw_{j} }$$

where T j,i,d,k is the air temperature in the grid point j for the 6 h-time interval i of the simulated day d corresponding to the model initialization k; \(\overline{T}^{i}_{j,k,d}\) is the mean daily temperature of the day d in the grid point j corresponding to the model initialization k; \(\overline{{\overline{T}^{i} }}^{k}_{j,d}\) is the mean daily temperature of the day d in the grid point j averaged over the model initializations reported in Table 2;

Table 2 Starting date of the weekly forecast for each analyzed month of the year 2010

Tw j is the mean weekly temperature in the grid point j; and Ta j is the mean weekly temperature averaged over the N grid points within the macro-area.

Since data are available every 6 h and resolutions are not extremely high, it is more appropriate to use daily mean temperatures rather than extremes. Moreover, using several runs with different model initialization may reduce uncertainties associated with individual runs. The multi-model ensemble of the e-kmf® global forecast system may also have an improved accuracy by reducing uncertainties associated with individual models. The same procedure (Figure 2) used for the e-kmf® model data output is applied for the CFS-NCEP model.

Figure 2
figure 2

Diagram of each step of the procedure for calculating the weekly temperature forecast T(a i ); Ini date is the date of the forecast initialization; Fct date is the date of the forecast day.

Data analysis

Different statistical performances are used to understand the predictability and reliability of temperature forecasts for each month in a perspective of 12 weeks ahead. The statistical analysis is computed for both forecast models and climatology mean (based on 1984–2008 data), by comparing them to the observations for each month of 2010. The indexes used and discussed in the following section are: the forecast error (FE) at given observed temperature values, the mean absolute error (MAE), the climatological Skill Score (SSclim), the anomaly correlation coefficient (ACC).

The forecasted error

The calculated forecasted error (Eq. 5) for each observed data is:

$${\text{FE}}_{i} = F_{i} - O_{i}$$

where: O i  = observed value; F i  = forecasted value.

Figures 3, 4, and 5 show the forecasting error in comparison with observed values for all the forecasted weeks of the year for the north, centre and south of Italy, respectively. These plots are used to illustrate the errors between forecasts and observation data according to a given temperature; in this way, we are able to control possible under/overestimation of the model depending on temperature values and it is possible to evaluate the performance of the forecasting model in different climate seasons.

Figure 3
figure 3

Forecast error vs. observed temperature values for the e-kmf® (blue rhombi) and the CFS-NCEP (red squares) model in the north of Italy; the two polynomial regressions are shown with a blue and red line, respectively for the e-kmf® and CFS-NCEP model.

Figure 4
figure 4

Forecast error vs. observed temperature values for the e-kmf® (blue rhombi) and the CFS-NCEP (red squares) model in the centre of Italy; the two polynomial regressions are shown with a blue and red line, respectively for the e-kmf® and CFS-NCEP model.

Figure 5
figure 5

Forecast error vs. observed temperature values for the e-kmf® (blue rhombi) and the CFS-NCEP (red squares) model in the south of Italy; the two polynomial regressions are shown with a blue and red line, respectively for the e-kmf® and CFS-NCEP models.

Figure 3 highlights how the CFS-NCEP model underestimates temperature forecasts in the north of Italy (about 4°C), while only a slight overestimation is provided by the e-kmf® model.

On the contrary, for the centre of Italy, the CFS-NCEP model shows an overestimation of temperature forecasts with values of less than 10°C (colder months) and an underestimation for temperatures greater than 10°C (warmer months); a similar trend, although less enhanced, was found for the e-kmf® model (Figure 4).

In the south of Italy, there is a significant temperature forecast overestimation below 12–13°C and an underestimation above 23°C by the CFS-NCEP model. The e-kmf® model shows an overestimation when the observed temperatures are under 10°C and no errors greater than ±3°C for warmer temperature values (Figure 5).

The mean absolute error

The MAE for the three macro-areas is shown in Tables 3 and 4 and calculated as follows (Eq. 6):

$${\text{MAE}}\; = \;\frac{1}{n}\sum\limits_{i = 1}^{n} {\left| {F_{i} - O_{i} } \right|}$$

where O i  = observed value; F i  = forecasted or climatological value, n = numbers of analyzed data.

Table 3 Mean absolute error of temperature (°C) for each model (e-kmf®, CFS-NCEP, Climatology) vs. area and month
Table 4 Mean absolute error of temperature (°C) for each week of forecasting between the e-kmf® and the CFS-NCEP model for each area of Italy

The computed values show lower errors for the macro-area of centre and south of Italy for the two meteorological models and climatological data. For the northern macro-area, the CFS-NCEP model highly underestimates the forecasted temperatures.

The reason for a lower MAE in the centre and south macro-area can be related to the forecast predictability which is higher in these two areas than in the northern one where the orography plays a relevant role; in fact, as it is shown in Figure 1, most of the grid points in southern area are over the sea surface and the topography is smoother than in the north. In addition to this first comparison, the MAE has been calculated as a mean of the ith weekly forecast of the 12 months in order to understand the reliability of forecast horizon for each model and macro-area. As can be seen from Table 4, the best score is obtained by the e-kmf® model in the first forecasting week, with a worsening of the performance between the 5th and 8th forecasting week as shown in Table 5 and Figure 3 as well. Table 6 shows the percentage of cases where the MAE of the temperature forecast is in selected ranges. These percentages have been computed on four classes: 0–1°C, 1–2°C, 2–4°C and >4°C. A MAE in the first two classes (between 0 and 1°C and 1–2°C) can be considered an excellent or good result, respectively, in terms of weekly prediction; the third class with forecast errors between 2 and 4°C may be considered a fair to a rather poor result and, finally, an error above 4°C may be considered a poor or a very poor achievement.

Table 5 ACC values for the e-kmf® and CFS-NCEP models for ith forecasting week in the three macro-areas

In particular, the e-kmf® model obtains a good performance: only 4% of the cases with a forecasting error above 4°C, while the CFS-NCEP model results were less satisfactory, especially in northern Italy, where 60% of the cases has a MAE above 4°C.

The climatological Skill Score

One of the most important scores used to evaluate the performance is the SSclim, which gives an idea of the relative improvement (or worsening) of the forecasting model in relation to certain reference values; the climatological mean has been used in this case study. The SS is calculated as follows (Eq. 7):

$${\text{SS}}_{\text{clim}} = \;\frac{{{\text{MSE}}_{\text{forecast}} - {\text{MSE}}_{\text{clim}} }}{{{\text{MSE}}_{\text{obs}} - \;{\text{MSE}}_{\text{clim}} }} = 1 - \frac{{{\text{MSE}}_{\text{forecast}} }}{{{\text{MSE}}_{\text{clim}} }}$$

where the MSE forecast, clim, and obs are the mean square error for the forecasted, climatological and observed data respectively and the MSE equation is calculated as follows (Eq. 8):

$${\text{MSE}}\; = \;\frac{1}{n}\;\sum\limits_{i - 1}^{n} {(F_{i} - O_{i} )^{2} } \;$$

As it is shown in Table 7, using the e-kmf® model there is a huge improvement for almost all months and for all areas: the three scores for the north, centre and south of Italy give an average improvement of 35% for the year 2010; this means that the e-kmf® model increases forecasting capability, with better forecasting results for 2-m air temperature of 35%, compared to the climatological averages. On the contrary, the CFS-NCEP model shows the opposite for almost all months and all areas, meaning that it would be better to use climatology to estimate seasonal temperature trends for the following weeks instead of the forecasting model.

Table 6 Percentage of cases where the mean absolute error of temperature forecasting is between 0–1°C, 1–2°C, 2–4°C and above 4°C for each area between the e-kmf® and CFS-NCEP models and the climatological mean for the year 2010

The anomaly correlation coefficient

Another important score is the ACC which gives an idea of the correlation between models and observed data, subtracting the climatological mean. In fact, another way to measure the quality of a forecasting system is to calculate the correlation between forecasts and observations. However, correlating forecasts directly with observations or analyses may give misleadingly high values, due to seasonal variations. It is therefore an established practice to subtract the climate average from both the forecast and the verification and to assess the forecast and observed anomalies according to the ACC.

The ACC is calculated as follows:

$${\text{ACC}}\; = \;\frac{{\sum\nolimits_{i = 1}^{n} {\left( {(F_{i} - C_{i} ) - \overline{(F - C)} } \right) \cdot \left( {(O_{i} - C_{i} ) - \overline{(O - C)} } \right)} }}{{\sqrt {\sum\nolimits_{i = 1}^{n} {\left( {(F_{i} - C_{i} ) - \overline{(F - C)} } \right)^{2} \cdot \left( {(O_{i} - C_{i} ) - \overline{(O - C)} } \right)^{2} } } }}$$

where: O i , F i , and C are the observed, forecasted and climatological values are the average values of the differences between observations or forecasts and climatological values for the analyzed data set. n = number of analyzed data.

Table 5 and Figure 6 (left) show how the e-kmf® model has a higher reliability for the first and third forecasting month (i.e. from the 1st to the 4th forecasting week and from the 9th to the 12th). On the contrary there is a worsening for the e-kmf® forecast in the 2nd month (i.e. from the 5th to the 8th week). For the CFS-NCEP model there is no general trend and very low values of ACC are shown in Figure 6 (right), i.e. no correlation at all between this model and observed data for every forecasting week, except for the first one.

Table 7 Climatological Skill Scores for the two models (e-kmf®, CFS-NCEP) and for each area and month
Figure 6
figure 6

ACC trends for the e-kmf® (left) and CFS-NCEP (right) models for ith forecasting week in three macro-areas of Italy.


Reliable meteorological forecasting in specific geographic areas could be a suitable support for improving operations in the energy market. A lot of progress has been made in the development of meteorological models and downstream applications, as well as forecast planning in gas and power supply and renewable energy generation in the last decade. From a long-term perspective, a meteorological seasonal forecast, which is often based on climatology, will be able to provide capability management in a time scale of just a few months.

As a major energy company, with the aim of improving the commercial planning of oil, natural gas and power, Eni has developed the kassandra meteo forecast (e-kmf®) model, i.e. a short to long term (from 1 to 90 days) proprietary meteorological forecast system in collaboration with the Epson Meteo centre. These new numerical models for temperature forecasting trends provide an alternative solution to statistical systems based on climatological data analysis. The e-kmf® meteorological model is based on the probabilistic approach of the ensemble technique and it will be used for energy resource management in different European regions. In fact, an accuracy improvement of forecasted temperature by about 1°C compared to values obtained by climatology may have a great benefit in gas supply portfolio management.

In this paper we evaluated the long-term temperature forecast performance of the e-kmf® and CFS-NCEP models in three regions in Italy (north, centre and south, excluding the main Italian islands) for the entire year 2010.

In particular, daily temperature forecasts collected from five daily initialization runs were averaged out to obtain a weekly forecast for each model grid point related to the three Italian macro-areas; afterwards, each temperature forecast of the model grid point was once again averaged in order to obtain a single temperature forecast value for each week (12 in total for each area). Statistical indexes have been used to calculate the performance analysis by comparing the observed data, the climatological mean and the two models that were analyzed.

According to the MAE the e-kmf® model performs better than the CFS-NCEP model in almost all areas and forecast initialization months. The SSclim index shows how the e-kmf® model has an average improvement of 35% compared with climatology (used as a reference) for the year 2010, while the performance of the CFS-NCEP is worse, in particular in the northern Italian macro-area where there is a significant mean underestimation (4.7°C using the mean absolute error).

The ACC provides information that is very useful for understanding the reliability of the forecast from the 1st to the 12th week for each forecast initialization month. In particular, the e-kmf® model shows a good correlation between forecasted and observed temperature data in the 1st and 3rd month of the forecast, while a worsening of the model’s performance was observed between the 5th and 8th week of prediction. This particular aspect will be investigated in more detail in order to improve the forecast for the entire period analyzed.



three-dimensional variational data assimilation


anomaly correlation coefficient


combined-cycle gas turbine


cooling degree day


Climate Forecast System–National Centers for Environmental Prediction


combined heat and power

e-kmf® :

eni-kassandra meteo forecast


forecast error


global data assimilation system


global forecasting system


global land data assimilation system


gridpoint statistical interpolation


heating degree day


mean absolute error


METeorological Aerodrome Report


mean square error


National Climatic Data Centre


National Oceanic and Atmospheric Administration


National operational model archive and distribution system

SSclim :

climatological Skill Score


sea surface temperature


surface SYNOPtic observations


weather research and forecasting–advanced research WRF


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Author’s contribution

AC worked on the benchmark analysis and data interpretation and he wrote most of the manuscript. GG wrote the background introduction and purposes of the paper. He presented an oral presentation regarding this study at the AOGS 2013 in Brisbane. RS developed the e-kmf model, collected all observed and climate data, and supervised all simulations of the model. GE has been involved in data model analysis and debugging. MM supervised the complete manuscript for important intellectual content and approved it for the final version to be published. All authors read and approved the final manuscript.


This research was carried out as part of the METEO Project funded by Eni. The authors are grateful to Dr. Michela Giorgetti and Dr. Roberto Vernazza for a fruitful scientific discussion.

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Correspondence to A Ceppi.

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Giunta, G., Salerno, R., Ceppi, A. et al. Benchmark analysis of forecasted seasonal temperature over different climatic areas. Geosci. Lett. 2, 9 (2015).

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