microwave sounding unit AOD Aerosol optical depth APOLLO AVHRR Processing scheme Over cLouds, Land and Ocean AROME Applications of Research to Operations at Mesoscale AROME

Keywords:

This deliverable has been prepared by AEMET within WP4 'Weather forecasting and measurement for renewable energy predictability'.

The present document describes the principles from both deterministic and probabilistic weather forecasting perspectives. It provides an overview of the numerical weather prediction models used for solar radiation forecasting in PreFlexMS project. It also establishes the forecasts and data formats used in PreFlexMS.

Chapter 2 presents the details of the deterministic forecasts while Chapter 3 shows a detailed description of the probabilistic forecast. Both kinds of products will be supplied to the project partners by AEMET and CENER. D4.3-Weather Forecast Requirements and Evaluation Methods H2020-PreFlexMS/ Grant no. 654984 5 D4.

Deterministic forecasts 1.1 Principles

The behavior of the atmosphere can be described by a set of hydrodynamic equations which express how the air moves, the process of heating and cooling, the role of moisture, etc. Numerical weather prediction is generally performed by numerical integration of the hydrodynamic equations governing atmospheric motions. These non-linear equations describing the evolution of the atmosphere do not have analytical solutions even if the problem is "well posed". If an analytical solution does not exist, we have to use the numerical techniques to find a certain approximation to the true solution of the system of equations and therefore we have to use computers. With the introduction of powerful computers in meteorology, the meteorological community has invested more time and efforts to develop more and more complex numerical models of the atmosphere.

Given a description of the current state of the atmosphere, numerical models can be used to propagate this information forwards to produce a forecast for future weather. The state of the atmosphere is described by the spatial distribution of wind, temperature, and other weather variables. By extrapolating the computed tendencies ahead in time, the model can predict the field variables in the future.

The initial conditions of any numerical integration are given by very complex assimilation procedures which estimate the state of the atmosphere by considering all available observations. The fact that a limited number of observations are available and that part of the globe is characterized by a very poor coverage introduces uncertainties in the initial conditions. A short-range forecast or first-guess provides an estimate of the atmosphere that is compared with the observations. The two fields are combined to obtain a correct atmospheric state called analysis. This process is named "Data Assimilation" (Figure 1).

In contrast to the original differential equations which describe the whole spectrum of atmospheric motions, the discretized equations describe only processes with certain spatial and temporal scales. Since subgrid-scale processes are not included in models, only their statistical effects on the mean flow are taken into account. The statistical contributions by the different processes must be expressed in terms of the large-scale parameters themselves. The mathematical procedure involved is called parametrization.

Therefore, the numerical modelling of the atmosphere is based on:

• Physics laws of Hydrodynamics • Statistical contributions of the subgrid-scale processes • Numerical methods • Use of powerful computers Numerical models face several specific problems:

• Uncertainties in the initial conditions • Many temporal and spatial scales • Non-linear systems • Insufficient knowledge of the physical laws as turbulent movement, microphysics of clouds, etc. There are several types of numerical models depending on the spatial and temporal scales considered. However, all models are based on the same hydrodynamic equations with initial conditions but with different parametrizations and horizontal and vertical resolutions.

Mesoscale models are used for short-range weather forecasts (0-2 days ahead). These models have a non-hydrostatic dynamical core and 1-3 km horizontal resolution. They produce forecasts few hours after observations are made. They are limited area models and their boundary conditions are given by a global model.

The global models are used for medium-range weather forecasts (2-15 days ahead). These models have a hydrostatic dynamical kernel. Both the parametrizations and the assimilation procedure are very important in them. They have more vertical levels than limited area models and the horizontal resolution is around 10-25 km. They produce forecasts up to several hours after observations are made. Numerical models calculate the heat transference due to short wave solar radiation and long wave emissions produced by atmospheric gases, clouds and the surface of the Earth.

The aim of each radiation parameterization is to provide a simple, precise and fast method to calculate the profile of total heating flux in the atmosphere. These estimations give:

• The total heating flux in the surface to calculate the superficial budget energy • The divergence of the horizontal and vertical radiative fluxes to calculate the heating and cooling in an atmospheric volume.

To build a radiation transfer scheme for a numerical model is required:

• A formal solution of the radiation transfer equation • An integration over the vertical, taking into account the variations of the radiative parameters with the vertical coordinate • An integration over the angle, to go from a radiance to a flux • An integration over the spectrum, to go from monochromatic to the considered spectral domain • A differentiation of the total flux to get a vertical profile of the heating rate Two models, HARMONIE (Hirlam Aladin Regional/Meso-scale Operational NWP In Europe), run by AEMET and IFS (Integrated Forecasting System), run by ECMWF (European Centre for Medium-Range Weather Forecasts) will be employed in this project as deterministic models.

The HARMONIE model

The HARMONIE model is being developed since 2005 by the ALADIN (acronym in French for Aire Limitée Adaptation Dynamique Initialisation) and HIRLAM (HIgh Resolution Limited Area Model) consortia in collaboration with the ECMWF (European Center for Medium Weather Forecast). The HIRLAM consortium is formed by Meteorological Institutes from Denmark, Norway, Sweden, Finland, Estonia, Iceland, Ireland, Lithuania, Netherlands and Spain. While ALADIN is a collaboration project of Meteorological Institutes of Algeria, Austria, Belgium, Bulgaria, Croatia, Czech Republic, France, Hungary, Morocco, Poland, Portugal, Romania, Slovakia, Slovenia, Tunisia and Turkey.

The HIRLAM consortium has developed a hydrostatic grid-point limited area model for the weather prediction up to 3 days with a spatial resolution of 5 to 16 km routinely. The dynamical core is based on a semi-implicit semi-Lagrangian discretization of the multi-level primitive equations, using a hybrid coordinate in the vertical (Unden et al, 2002 and http://hirlam.org/index.php/hirlam-programme-53/general-model-description/synoptic-scalehirlam/48-general-model-description/synoptic-scale-model-hirlam?layout=blog).

ALADIN is a limited-area spectral model. The vertical coordinate is a hybrid coordinate. ALADIN needs to be forced by a global model which has to provide lateral boundary conditions; the lateral forcing is done according to a Davies relaxation [START_REF] Davies | A lateral boundary formulation for multi-level prediction models[END_REF]. ALADIN is generally used with a plane projection (one can currently use a conformal Lambert projection of a Mercator projection). When using ALADIN with a domain which is not too big, the horizontal grid is a quasi-regular grid (the mapping factor M has only weak variations and remains close to 1). Some applications can require a big domain where M can become significantly greater than 1. Operational exploitation of ALADIN at METEO-FRANCE is now limited to overseas French territories.

AROME (Applications of Research to Operations at Mesoscale

) is a limited-area model designed for horizontal mesh-size around 1 to 2.5 km. It takes most of the ALADIN code concerning the adiabatic part of the code (in particular the non-hydrostatic code), the main difference with the current version of ALADIN being the physics package. AROME uses a physics package well adapted for small mesh-sizes around 1 km, this physics package is mainly an adaptation of the one which is currently used in the non-hydrostatic research model MESO-NH (used by the team CNRM/GMME for research applications). AROME is used operationally at METEO-FRANCE.

HARMONIE is a mesoscale model which main characteristics are a spectral horizontal formulation with a bi-Fourier function basis, a hydrostatic-pressure hybrid vertical coordinate and a non-hydrostatic (NH) dynamical kernel from ALADIN NH model [START_REF] Bénard | Dynamical kernel of the Aladin-NH spectral limited-area model: Revised formulation and sensitivity experiments[END_REF]. The physics can use three types from AROME [START_REF] Seity | The AROME-France convective-scale operational model[END_REF] for high resolution, from ALADIN and from HIRLAM both for synoptic scales. Its horizontal resolution is 2.5 km and 65 vertical levels. It can produce weather predictions up to 2 days with a variable spatial resolution depends on the physics used. In Figure 2, the scheme of the flow is presented. HARMONIE contains the dynamics from ALADIN. For the physics, HARMONIE can use three different schemes depending on the spatial resolution:

• HIRALD from HIRLAM for synoptic scales up to 5 Km • ALARO from ALADIN for synoptic scales up to 3 Km • MESO-NH from AROME with a resolution of around 1 to 2.5 Km

In the AEMET version of HARMONIE, the AROME physic used is adapted from the MESO-NH research model [START_REF] Lafore | The meso-NH atmospheric simulation system. Part I: adiabatic formulation and control simulations[END_REF]. AROME/HARMONIE includes twelve 3D variables, a sophisticated microphysics scheme (ICE3 [START_REF] Pinty | A mixed-phase cloud parameterization for use in mesoscale non-hydrostatic model: simulations of a squall line and of orographic precipitations[END_REF], three precipitation states (rain, snow and graupel), and turbulence from the HARATU scheme [START_REF] Lendering | An updated length-scale formulation for turbulent mixing in clear and cloudy boundary layers[END_REF]. The Eddy-Diffusivity Mass-Flux (De Rooy and Siebesma, 2010) is used to compute the convection in the boundary layer. Surface processes are based on the ISBA and TEB schemes [START_REF] Noilhan | A simple parameterization of land surface processes for meteorological models[END_REF][START_REF] Noilhan | A simple parameterization of land surface processes for meteorological models[END_REF][START_REF] Masson | A physically-based scheme for the urban energy budget in atmospheric models[END_REF]. In addition, the assimilation data used in HARMONIE is a 3D-Var scheme [START_REF] Fischer | An overview of the variational assimilation in the Aladin/France NWP system[END_REF] that is very similar to the IFS and ARPEGE assimilation methods. For more information see [START_REF] Calvo | HARMONIE, el nuevo modelo de alta resolución de AEMET[END_REF]Navascues et al., 2013. In Figure 3, the areas of the different operative models are shown. The radiation scheme used in HARMONIE is the ECMWF IFS cycle 25R1 [START_REF] Morcrette | Radiation and cloud radiative properties in the ECMWF operational weather forecast model[END_REF][START_REF] White | ECMWF: IFS Documentation Cycle CY23r4, Part IV: Physical processes[END_REF], also described in http://www.ecmwf.int/sites/default/files/elibrary/2003/13280part-iv-physical-processes.pdf). It considers six short wave (SW) spectral bands from the ultraviolet (UV) to the solar infrared (IR) range [START_REF] Mascart | The Meso-NH atmospheric simulation system: Scientific documentation[END_REF][START_REF] White | ECMWF: IFS Documentation Cycle CY23r4, Part IV: Physical processes[END_REF], where the solar radiation is attenuated by absorption gases (H 2 O, O 2 , CO 2 , CH 4 , N 2 O and O 3 ) and scattered by atmospheric molecules, aerosols and clouds. In the long wave (LW) part of the spectral range, 16 bands cover atmospheric windows as well as spectral regions where the effects of H 2 O, CO 2 and O 3 are important.

The SW scheme assumes a plane parallel atmosphere and solves the radiation transfer equations based on the work of Fouquart and Bonnel (1980). It uses Delta-Eddington twostream approximation and adding method for radiative transfer. The inherent optical properties of the atmospheric molecules and aerosols are obtained from statistical models using parameters derived from the HITRAN database (Rothman et al., 1986[START_REF] Rothman | The HITRAN molecular database: Editions of 1991 and 1992[END_REF]. Monthly mean aerosol optical depth at 550 nm from six aerosol types are included based on the work of Tegen, 1997.

The Rapid Radiation Transfer Model (RRTM) is used in the LW radiation scheme in order to accurately compute fluxes and heating rates. RRTM uses the correlated-k method [START_REF] Lacis | A description of the correlated kdistribution method for modeling nongray gaseous absorption, thermal emission, and multiple scattering in vertically inhomogeneous atmospheres[END_REF][START_REF] Fu | On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres[END_REF]. The scheme assumes a non-scattering atmosphere in local thermodynamic equilibrium. The effect of clouds on the fluxes is implemented based on [START_REF] Washington | A description of the NCAR GCMs[END_REF]. [START_REF] Morcrette | On systematic errors in parametrized calculations of longwave radiation transfer[END_REF], narrow-band model was used to evaluate the band fluxes in these spectral regions.

Weather forecast models need to know the current state of the atmosphere and the Earth´s surface to be initialised. The quality of the forecast strongly depends on the accuracy of the observed data assimilated in the models. Data from numerous satellite instruments, weather stations, ships, buoys, and other components are assimilated in the models to determine a best possible atmospheric and Earth´s surface state.

The HARMONIE assimilation scheme has been developed by HIRLAM and ALADIN consortia and allows to use 3DVar or 4DVar schemes. AEMET AROME/HARMONIE assimilates observations from the two previous hours to one hour after the nominal analysis time. The assimilated data come from SYNOP, SHIP, TEMP, AIREP, DRIFTER, DRIBU and PILOT, as well as raw radiance from the ATOVS satellite (AMSU-A, AMSU-B and MHS sensors). Nowadays also hourly GPS data is used in an experimental version. In addition, the large scale flow is improved by mixing the large scale variables from the ECMWF with the high resolution variables from HARMONIE. The process maintains the HARMONIE surface fields already analysed by an Optimum Interpolation scheme.

The blending of the global and limited area fields is carried out by means of digital filter methods. The blending method improves the quality of the first guess because:

• The biggest errors are mainly caused by the large scale which is, currently, much better represented by the global model due to the better quality of the analysis and the big amount of observations, especially the satellite measurements. • The small scale fields from HARMONIE are preserved and • The boundary conditions are updated in every cycle.

Nowadays, AEMET is using the version 40h1 operationally that provides hourly outputs up to 48-hour forecast length. Compared to the previous version, changes have been made to the optical properties of water clouds in the radiation scheme for solar radiation in order to improve the model's transmission of solar radiation through water clouds. In addition the parameterization of cloud inhomogeneity is no longer applied in view of a high model resolution compared with previous low resolution models requiring such formulation.

Description of HARMONIE deterministic cycle

AROME/HARMONIE model is run eight times every day. At 00, 06, 12 and 18 UTC the model is run up to a range of 48 hours and at 03, 09, 15 and 21 UTC the model is run only for the first 6 or 12 hours for nowcasting. This model scheme was called RUC3 in previous documents. The boundary conditions (BCs) are available from the IFS model every 6h, and observations are assimilated using the 3D-var technique taking a window of 3 hours around the nominal time (from -2 to +1 hours). There is a short interval since the end of the assimilation window until the start of the run to guarantee every observation for that window has arrived. E.g. the 00 UTC Harmonie run is started actually at 1:30 UTC allowing the observations up to 00 UTC to come in, being quality controlled and pre-processed -it will process the atmospheric state from 00 UTC onwards. The output is available approximately 3 hours after the nominal time (Figure 4).

Description of the hourly Rapid Updated Cycle

The hourly Rapid Updated Cycle (RUC1) will be an assimilation system that will provide forecasts of the first 12 hours and will run every hour. RUC1 will assimilate the most recent available observations in order to update the current conditions providing, in that way, more accurate initial conditions to the main cycle of the model (Figure 5). Furthermore, RADAR precipitation and wind products will be introduced in the assimilation cycle. Data will be assimilated within a window around the nominal time of about -30 to + 30 minutes and the output will be available about 1.5 hours after the nominal time. The RUC system is being developed now. The forecasts provided by this system will be an important tool for severe weather forecast and for special user such as the aviation community. Although it is out of the scope of the project, some tests will be carried out to verify its accuracy if it becomes operational in time.

The ECMWF/IFS model

The deterministic or high resolution IFS is a global model (http://www.ecmwf.int/en/research/modelling-and-prediction) that provides 3-hour outputs up to ten days forecast length. The dynamical core of IFS is hydrostatic, two-time-level, semiimplicit, semi-Lagrangian and applies spectral transforms between grid-point space (where the physical parametrizations and advection are calculated) and spectral space. In the vertical the model is discretized using a finite-element scheme with 137 vertical levels. A Gaussian reduced grid is used in the horizontal with resolution of about 0.1°. The IFS also has extra configurations available for research experiments that are not used operationally (http://www.ecmwf.int/en/research/modelling-and-prediction/atmospheric-dynamics).

The physical processes associated with radiative transfer, convection, clouds, surface exchange, turbulent mixing, subgrid-scale orographic drag and non-orographic gravity wave drag have a strong impact on the large-scale flow of the atmosphere. However, these mechanisms are often active at scales smaller than the resolved scales of the model grid. Parametrization schemes are then necessary in order to properly describe the impact of these subgrid-scale mechanisms on the large-scale flow of the atmosphere. In other words the ensemble effect of the subgrid-scale processes has to be formulated in terms of the resolved grid scale variables. Furthermore, forecast weather parameters, such as two-meter temperature, precipitation and cloud cover, are computed by the physical parametrization part of the model (http://www.ecmwf.int/en/research/modelling-and-prediction/ atmospheric-physics).

The radiation scheme is based on the RRTM [START_REF] Mlawer | Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave[END_REF][START_REF] Iacono | Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models[END_REF]. The SW and LW radiative fluxes are computed using climatologies of trace gases and aerosols, for the temperature, humidity and cloud prognostic parameters are used. The interaction between cloud and radiation is computed based on McRad method [START_REF] Morcrette | Impact of a new radiation package, McRad, in the ECMWF integrated forecasting system[END_REF].

Data sent from AEMET to CENER 1.4.1 Parameters

The parameters provided to CENER are shown in Table 1 and2 for the data predicted by HARMONIE andin Table 3 and4 by ECMWF. Harmonie radiation parameters (116 and117) represent the short-wave radiation, emitted by the sun that reaches the Earth surface after been scattered, absorbed or transmitted by a square-meter of a flat horizontal plane atmosphere. The parameter 117 is the total horizontal radiation, therefore it is the radiation which would be measured by a global pyranometer. Parameter 116 is the direct horizontal radiation that reaches the surface without interacting with the atmosphere. Note that this parameter does not represent the Direct Normal Irradiance (DNI), so the DNI needs to be calculated by means of a post-process method. Both parameters (117 and 116) are accumulated from the beginning of the model integration, meaning that i.e. for t=1 h, the 117 parameter would be the global radiation reaching the surface during the first hour of prediction, while for t=24 h the 117 parameter would be the same but for the first 24 hours, in units of Jm -2 . Accumulated radiation for a specific time interval can be calculated by subtracting the values of radiation for two consecutive intervals. Cloud parameters such as the total, low, medium and high cloud are instantaneous parameters at the nominal time, therefore there might be differences with the radiation parameters in the sense that a cloudy grid point at the nominal time might present non null values of accumulated radiation. Note that wind parameters are prognostics at 10 m and are averages of the last 10 minutes before the nominal time, as already explained in the deliverable D4.1.

The temperature is the instantaneous temperature at 2m height, the relative humidity is the same at 2m and pressure is an instantaneous surface parameter.

Vertical profile parameters (200m wind, 10m and 200m temperature) are not provided directly by the model, and will be calculated by means of vertical interpolation from model level parameters or other algorithms (Table 2). For the ECMWF model, there is a list of equivalent parameters (Table 3). In this case the global radiation is represented by parameter 169, and the direct horizontal radiation by parameter 228021. 200m wind, 10m and 200m temperature will be calculated as in the Harmonie case (Table 4).

Temporal availability

AEMET has provided CENER with data from year 2015 for training purposes: HARMONIE hourly data up to H+48h run every 6 hours (00, 06, 12 and 18 UTC cycles) and ECMWF 3-hourly data up to H+72 run at 00 and 12 UTC cycles.

For the operational phase of the project, the HARMONIE data will be generated with the version 40h1. If the normal cycle is selected, the model will provide 15 minutes output run every 3 hours (00, 03, 06, 09, 12, 15, 18 and 21 UTC cycles), see The ECMWF data is 3-hourly data up to H+72h run at 00 and 12 UTC cycles during both the training and the operational phases (Table 5). ECMWF data is available about 7 hours after the nominal time.

Data format

The output is provided to CENER using grib files (version 1), covering an area over the Iberian Peninsula from 37.5° to 40° of latitude and from -9° to -6° of longitude (Figure 6). The original HARMONIE files follow a Lambert conformal projection, and have a horizontal grid resolution of around 2.5 km. The data is delivered to CENER after being interpolated to a latitudelongitude (lat-lon) projection with a resolution of 0.025°. Native data from the ECMWF model is provided in octahedral O1280 grid, and it is interpolated to a lat-lon projection with a resolution of 0.1°, around 9 Km of horizontal resolution.

Forecasts provided by CENER to partners for R&D

The operation and management tasks involved in the CSP plants imply that the industry demands high temporal resolution for the DNI forecasted. Besides, it is required a detailed adaptation to the site dynamics of DNI more precise than global trends currently provided by NWP models. The high variability of atmospheric phenomena, the complex atmospheric modeling on which NWP relies, the extremely large underlying systems for data capture and assimilation and, in general, the large uncertainty associated with weather behavior make accurate localized and high-frequency forecasting a very difficult task. It is worth to highlight that the variability of DNI is also strongly dependent on the local microclimate. In this section, DNI and weather data to be provided by CENER in the frame of this project as well as time resolution requirements is detailed.

Parameters

The key parameter to be provided by CENER is Direct Normal Irradiance (DNI). This variable can be provided based on the Direct Model Output (DMO) from AROME/HARMONIE or ECMWF based on temporal interpolations only . A comparison analysis between measured and forecasted DNI data will be applied on historical local measurements, in order to estimate the uncertainty of the DNI data to be provided. Different probabilities of exceedance (10, 25, 75, 90) will be calculated on the differences between these datasets, and also they will be broken down into categories of solar elevation and beam clearness index (the ratio of actual DNI to its corresponding clear sky value). Finally, probabilities of exceedance 10, 25, 75 and 90 of these differences will be also provided by CENER together with the forecasted DNI, as a function of its beam clearness index and solar elevation.

In addition to DNI and its uncertainty, CENER will provide weather parameters which influence solar thermal plant performance, as air temperature, wind speed and direction.

Temporal availability

High-frequency DNI series allow an accurate modeling and analysis of transient processes in some CSTP technologies, which show a nonlinear response to DNI governed by various thermal inertias due to their complex response characteristics.

In this project, CENER will provide DNI and weather parameters at 15-min time resolution. This temporal resolution is provided in this project by AROME/HARMONIE, but unfortunately it is not available in ECMWF, that provides parameters at 3-hourly intervals making it necessary a procedure for increasing its temporal resolution.

DNI is the only variable to be provided by CENER in this project that is truly intermittent, since it can vary from values of ~1000 W/m 2 to zero in seconds, as is it strongly influenced by passing clouds. Consequently, a high-performance method will be applied to increase the temporal resolution from 3-h forecasted and post-processed DNI series to 15-min that dynamically assemble site information to provide high frequency DNI series (up to the temporal resolution of available measurements at the site; [START_REF] Peruchena | Generation of series of high frequency DNI years consistent with annual and monthly long-term averages using measured DNI data[END_REF][START_REF] Fernández-Peruchena | Increasing the temporal resolution of direct normal solar irradiance series in different climatic zones[END_REF]. The rationale for this data-driven approach is that patterns exist in the historical dataset that can be used for characterizing high frequency DNI dynamics at the site. This methodology provides a similar dynamic behavior than measured ones, by generating both peak amplitude and duration similar to those observed. Figure 7 shows measured (red) and generated from 3h series (blue) 1-min DNI series in different day types. Given the dynamics behavior of the other weather parameters involved, a linear interpolation will be carried out to increase their temporal resolution from 3-h to 15-min.

Data disposability for deterministic forecast and files characteristics are shown in Table 6. It will depend on the NWPM availability, in case of Harmonie model 4 runs per day are available meanwhile ECMWF present two runs. The time delivery of the forecast must be added to the time execution to know the daily scheduled delivery.

Data format File Name

Each new prediction will be delivered in a file whose name will contain value information about its containing and origin. The name of the files is also designed to easy its management by automatic processes. So, the name of the file will contain 6 frames separated by the character "_" like is shown in the next example: EC_ML1_Evora_20150101_00_det.cnr

• Two characters to identify the NWPM involved in the prediction. For example EC for the ECMWF model. • Three characters to identify the post process used in the prediction. For example ML1

for the version 1 of the Machine Learning. • Five characters to identify the emplacement. In this case Evora.

• Eight characters for the date of forecast in format yyyymmdd.

• Two characters to identify the methodologic cycle. In this case a prediction generated at 00. • Three characters to identify the kind of information, det for deterministic and prb for probabilistic.

• The extension of the file will be .cnr

File format

The predictions are delivered in plain text files, with the information presented in columns and tab as separator. As first option the delivery will be made without compression but, if it was necessary it could be sent in zip format or similar. The first row of each file corresponds with the name of the columns.

Deterministic forecast outputs.

Table 7 contains the information of each column: Name, data format and a brief description of the data value.

DatePred yyyymmddhhMM

The predicted date (UTC). It contains four digits indicating the year (yyyy), two digits indicating the month (mm), two digits indicating the day (dd), two digits containing the hour (hh) and two digits indicating the minute (MM)

Step

Float

The horizon of forecast. That is, the step ahead which the prediction is made. Additional required meteorological variables will be added as successive columns from wind direction column. The error code for any variable is -999. for float and -999 for integer variables.

Lat

Forecasts provided by CENER during the demonstration phase

The format and information delivered will be the same when the aim is the demo activities or the R&D ones. The main difference is that in case of demo, periodic deliveries will be made coinciding with each new NWPM output availability, as is described in Table 6, meanwhile in case of R&D activities the delivery will be formed by one historic of forecasts. This historic will contain a simulation of operative forecast deliveries with the same temporal resolution and variables that those of the demo case.

Probabilistic forecasts 2.1 Principles

The atmospheric movements can be described by non-linear differential equations that unfortunately have no analytical solution. The numerical methods to solve them have been developed in different stages. During the 50s was demonstrated the close relation between cyclone dynamics and the global circulation using a 2-layer model. At the beginning of the 70s, the global circulation models emerged [START_REF] Lynch | The ENIAC Integrations[END_REF], which are based on a set of non-linear differential equations, called primitive equations. During the 80s, regional and mesoscale numerical models appeared [START_REF] Athens | Development of hydrodynamic models suitable for air pollution and other mesometeorological studies[END_REF][START_REF] Mesinger | The step mountain coordinate: model description and performance for cases of alpine cyclogenesis and for a case of an Appalachian redevelopment[END_REF] and the 90s, atmosphere-ocean and atmosphere-ocean-soil coupled models allowed the development of diagnostic techniques for weather forecasting [START_REF] Davis | Potential Vorticity Diagnostics of Cyclogenesis[END_REF][START_REF] Stein | Factor Separation in Numerical Simulations[END_REF][START_REF] Mechoso | General ciculation. Models[END_REF].

This evolution on numerical weather prediction is a direct consequence of the increase of computer power, the spatio-temporal high resolution of the models and the improvement in observational networks and assimilation methods. All of this contributed to extend the knowledge on the dynamics and microphysical processes in the atmosphere.

Until then, the numerical weather prediction (NWP) philosophy was based on the deterministic atmospheric behaviour. That means, given an initial state of the atmosphere, its time evolution can be numerically predicted to give a final state, which is unique. Accordingly to this premise, a deterministic system is one in which the chance is not involved in any future states of the system. As a consequence, a deterministic model will always lead to the same final state from identical initial conditions. Consequently, the efforts of the scientific community on NWP were focused on producing the most accurate forecast [START_REF] Tracton | Operational ensemble forecasting prediction at the National Meteorological Centre: Practical aspects[END_REF]. [START_REF] Lorenz | Deterministic nonperiodic flow[END_REF] showed the concepts of Chaos Theory using a simplified model of fluid convection to numerically represent a dynamical system that exhibits most of the properties of other more complex chaotic systems. Lorenz demonstrated that small variations on the model initial conditions (ICs) do not produce a single final solution but a set of different possible solutions. Consequently, due to the chaotic nature of the atmosphere, different sources of uncertainty (error) can be defined in NWP within the forecast chain:

Uncertainty sources in Numerical Weather Prediction

• ICs forecast error source: Forecast errors can arise due to inaccuracies in the characterization of the initial atmospheric state. • Model formulation forecast error source: Due to inadequacies of NWP models on its own. • Parameterization forecast error source: Processes that occur at spatial scales finer than the model spatio-temporal resolution the model works with must be parameterized by empirical formulations leading to another source of uncertainty.

• LBCs forecast error source: When limited-area models (LAM) are used to design LAM ensemble prediction systems (LAMEPS), lateral boundary conditions (LBCs) coming from global NWP models are another source of forecast error.

Errors are amplified as the forecast period grows and will evolve into spatial structures shaping the flow of the day. The inherent atmospheric predictability is thus state-dependent and that is why the predictability of the future atmospheric states is also limited in time [START_REF] Lorenz | Deterministic nonperiodic flow[END_REF][START_REF] Lorenz | The predictability of a flow which possesses many scales of motion[END_REF].

Observational methods, assimilation strategies and the own characteristics of numerical models have inherent limitations that introduce uncertainty in the estimation of the possible future atmospheric states. This uncertainty misleads the forecast and is amplified when the forecast period grows and when the spatio-temporal resolution of the model increases.

Therefore, the atmospheric state cannot be exactly known because the forecast chain always contains uncertainties, which only can be estimated. The inaccurate determination of the real atmospheric state leads to the existence of a set of initial conditions compatible with it. A single model only provides a single solution of the future atmospheric state.

The traditional deterministic approach gave way to a new paradigm with richer information than a single solution of the future state of the atmosphere. The new paradigm includes quantitative information about the uncertainty (errors) of the predictive process. The atmospheric non-linear behaviour, consequently chaotic, must be treated now in a probabilistic way by means of the generation of multiple forecasts starting from slightly different but equally probable initial conditions in order to characterize the uncertainty of the prediction [START_REF] Leith | Theoretical skill of Monte Carlo forecast[END_REF].

To capture these sources of uncertainty, many operational and scientific centres worldwide produce ensemble forecasts (e.g. NCEP, ECMWF, etc.) since the early of 1990s. The basic idea behind ensemble forecasting is to run multiple (ensemble) forecast integrations from slightly perturbed ICs (ICs forecast error source) coming from multiple models and/or perturbing model formulation (model formulation forecast error source).

Initial conditions forecast error source

A limitation of numerical weather prediction is the lack of observational data with high enough resolution to properly describe the initial state of the atmosphere. Although the model could perfectly simulated all the atmospheric processes, it would be impossible to determine a realistic initial state description of the atmosphere for all resolutions at all times and everywhere using the available observational data [START_REF] Daley | Atmospheric Data Analysis[END_REF]. Another contribution associated to the observational error is related to the inherent error of any sampling procedure and instrumental error when observations are recorded and processed.

The data assimilation strategy suitably selected for the generation of an initial state of the atmosphere will be also affected by errors coming from both the set of observations used in the analysis and the short-range model forecast used as first guess. The data assimilation process represents a cycle that extracts information content from the observations scattered in place and time and move that information to the model grid while preserving the interrelated physical, dynamical and numerical consistency required for the model to make a good forecast. The resulting objective analysis from the data assimilation process blends information from observations with short-range forecast about small-scale processes (such as topographic effects) and past observations from the previous time through the cycle. This new analysis provides initial conditions for the next operational short-term forecast and is used to blend with the next set of observations to start the cycle again.

Model formulation forecast error source

The model formulation is a simplified scheme of what really happens in the atmosphere as a consequence of our inability to solve numerically the physical laws that governing the atmospheric motion. Contributions to this forecast-error source are related to the dynamical formulation of the model, the numerical method employed to integrate the model equations, the horizontal and vertical model discretization resolutions and the methodology used to make the discretization itself.

Parameterization forecast error source

Although the improvement of numerical models permits an even better characterization of the atmospheric processes the model itself will always have some limitations related to the scales of known processes that cannot be explicitly resolved using the spatio-temporal resolutions the model works with. These processes must be parameterized or simulated and these approximations made to solve numerically the empirical equations generate errors associated to the parameterization schemes used in the model.

The model cannot explicitly solve turbulence in the planetary boundary layer, the ground energy budget, convection or cloud microphysical because they occur at a finer scale than the spatio-temporal resolution of the model. All these processes are called sub-grid processes. A parameterization is the statistical method used to take into account the sub-grid processes by the model. Parameterizations are imperfect representations of atmospheric processes so they always mislead the model [START_REF] Tribbia | The reliability of improvements in deterministic shortrange forecasts in the presence of initial state and modeling deficiencies[END_REF][START_REF] Palmer | On parameterizing scales that are only somewhat smaller than the smallest resolved scales, with application to convection and orography[END_REF].

Lateral boundary conditions forecast error source

The LBCs forecast error source is only present in limited-area models or regional models, which use as inputs lateral boundary values spatially and temporally interpolated from global models, either by a coarser resolution grid or spectral model. Errors from global models are translated into LAM as LBCs error forecast source.

Ensemble prediction techniques

A practical approximation to probabilistic forecasting based on meteorological models is the so-called ensemble forecasting methodology. The ensemble prediction system (EPS) is a tool for estimating the time evolution of the Probability Density Function (PDF) viewed as an ensemble of individual selected atmospheric states. Each of these initial different states is physically plausible. The spread of the states is representative of the prediction error/uncertainty [START_REF] Toth | Ensemble forecasting at NCEP: The breeding method[END_REF].

If an idealized EPS could be generated that just properly captures all sources of forecast error (uncertainty), then the forecasted PDF would be reliable and skilful, that is, sharper than the climatological PDF. No further information is needed to become trustworthy the forecast-error predictions since a perfect PDF is a complete statement of the actual forecast uncertainty.

These errors are particularly pronounced when dealing with mesoscale forecast of nearsurface weather variables leading to large under-dispersion results because of the insufficient ensemble size, inadequate parameterization of sub-grid scale processes and inaccurate knowledge of land-surface boundary conditions [START_REF] Eckel | Aspects of effective mesoscale, short-range ensemble forecasting[END_REF]. Even so, realensemble forecast distributions often represent a substantial portion of the true forecast uncertainty although they were generated from an incomplete representation of weather forecast error sources.

EPS techniques used by global models

EPS are used operationally in several weather and climate prediction centres worldwide.

Several techniques for constructing an ensemble have been developed and applied on operational and research modes by different meteorological services. For many years, operational forecasters routinely compare forecasts from different global NWP Centres to assess the confidence in the predictions of their own models and to take into account alternative forecasts. This set of available products is often called the Poor Man's ensemble [START_REF] Ebert | Ability of a Poor Man's Ensemble to Predict the Probability and Distribution of Precipitation[END_REF] or ad hoc ensemble by some other authors, because its production is relatively chip compared to the cost of developing and running a full EPS such as the European Centre for Medium Range Weather Forecast (ECMWF) and the National Centres for Environmental Prediction (NCEP) ones. These ensembles are cheap and easy to create, but they are not generated in a controlled and systematic approach, because of that they are not calibrated and also some ensemble members may be always quite more skilful than others. Therefore, its major drawback is that the hypothesis of equally probable ensemble members is less guaranteed than other EPS strategies.

One of the first methods proposed for generating an ensemble of initial states of the atmosphere is the random Monte Carlo statistical methodology [START_REF] Leith | Theoretical skill of Monte Carlo forecast[END_REF][START_REF] Hollingsworth | An experiment in Montecarlo Forecasting[END_REF][START_REF] Mullen | The impact of initial condition uncertainty on numerical simulations of large-scale explosive cyclogenesis[END_REF]. This technique consists of sampling all sources of forecast error by perturbing any input of the system such as the analysis, initial conditions, boundary conditions, etc. The main limitation of the Monte Carlo approach is the need to perform a high number of perturbations in order to describe properly the initial uncertainty, which is usually far from the available computational resources. This limitation leads to a reduced sampling that identifies active components that will dominate forecast error growth.

Another EPS approach is the Lagged Average Forecast (LAF) technique proposed by [START_REF] Hoffman | Lagged average forecasting, an alternative to Monte Carlo forecasting[END_REF]. The time-lagged methodology uses forecasts from lagged starting times as ensemble members, which are easy to construct but they lack any scientific motivation. LAF method has the disadvantage that earlier forecasts often are statistical significantly less skilful than later forecasts. This drawback can be partly resolved by either using different weights for different ensemble members or by scaling back larger errors to a reasonable size. This methodology is the basis of the Scaled Lagged Averaged Forecast (SLAF) technique [START_REF] Ebisuzaki | Ensemble experiments with a new lagged average forecasting scheme[END_REF].

Initial condition forecast error source have a dominant effect up to the 12h forecast period.

Several EPS approaches used by NWP have been developed based on perturbed methods, which depend on the atmospheric flow. Strategies such as singular vectors and breeding vectors generate perturbations in the subspaces where initial conditions errors grow faster are generated.

The ECMWF singular vector method [START_REF] Palmer | Ensemble prediction[END_REF][START_REF] Molteni | The ECMWF Ensemble Prediction System: Methodology and Validation[END_REF] tries to identify the most dynamically unstable regions of the atmosphere by calculating where small initial uncertainties would affect a 48h forecast most rapidly (Figure 8). Singular vectors give a sampling of the perturbations that produce the fastest linear growth in the future [START_REF] Buizza | The singular vectors structure of the atmospheric general circulation[END_REF][START_REF] Hamill | A comparison of probabilistic forecasts from bred, singular-vector, and perturbed observation ensembles[END_REF]. There are only a relative small number of directions in the phase-space of the atmospheric system along which the most important processes occur. Maximum growth is measured in terms of total energy.

An alternative to the ECMWF's singular vector approach is the NCEP breed mode (Toth andKalnay, 1993 and[START_REF] Palmer | On parameterizing scales that are only somewhat smaller than the smallest resolved scales, with application to convection and orography[END_REF][START_REF] Tracton | Operational ensemble forecasting prediction at the National Meteorological Centre: Practical aspects[END_REF]. A random perturbation is added to the initial analysis. This perturbation evolves in time by integrating the forecast model, then is rescaled and reintroduced as a new perturbation. After several cycles, only the fastest growing errors remain. Breeding vectors give a sampling of the growing analysis error (Figure 9).

Figure 9: Breeding Cycle

In addition to the singular and breeding vector methods there are the Ensemble Transform Kalman Filter (ETKF) technique by [START_REF] Bishop | Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects[END_REF] and [START_REF] Wang | A comparison of breeding and ensemble transform Kalman filter ensemble forecast schemes[END_REF] used by the UK Meteorological Office (Met Office); and the Ensemble Data Assimilation (EDA) technique [START_REF] Houtekamer | A system simulation approach to ensemble prediction[END_REF][START_REF] Buizza | Potential use of an ensemble of analyses in the ECMWF Ensemble Prediction System[END_REF]. ETKF is similar to breed vectors except that a transformation matrix replaces the rescaling factor what it leads to an improved ensemble dispersion growth. The other hand, EDA creates an ensemble of assimilations coming from different analyses, which have been previously generated by observations randomly perturbed in a consistent manner with observation error statistics.

Model forecast error source coming from model formulation and parameterization schemes is another source of uncertainty to take into account in the forecast process. Several techniques haven been developed to address this issue. The Multi-Model or the Multi-Model Super-Ensemble approach [START_REF] Krishnamurti | Improved weather and seasonal climate forecast from multimodel superensemble[END_REF]) is a powerful method to construct EPS based on weighting different model outputs in order to set weather parameters. Weights are estimated performing a least squares adjustment for a so-called training period. The Multi-Model method implies equally probable ensemble members, which does not always occur. The Multi-Parameterization or Multi-Physics approach [START_REF] Stensrud | Ensemble forecasting of mesoscale convective systems[END_REF][START_REF] Houtekamer | A system simulation approach to ensemble prediction[END_REF][START_REF] Houtekamer | Data assimilation using an ensemble Kalman filter technique[END_REF][START_REF] Andersson | The ECMWF implementation of the three-dimensional variational assimilation (3D-Var). III: Experimental results[END_REF] consider the model sub-grid scale uncertainty by means of varying model physical parameterizations. The Stochastic Parameterization approach [START_REF] Buizza | Stochastic representation of model uncertainties in the ECMWF Ensemble Prediction System[END_REF][START_REF] Lin | Considerations for stochastic convective parameteriza-tion[END_REF] applied at ECMWF is based on perturbing the parameterized tendencies on a stochastically mode by a multiplicative noise. The Multi-Parameter approach [START_REF] Murphy | Quantification of modelling uncertainties in a large ensemble of climate change simulations[END_REF] tries to capture the significant uncertainty associated to some parameters of the model changing the values of those parameters in each ensemble member. Finally, the Stochastic-Kinetic Energy-Backscatter approach [START_REF] Shutts | The use of high resolution numerical simulations of tropical circulation to calibrate stochastic physics scheme[END_REF][START_REF] Shutts | A kinetic energy backscatter algorithm for use in ensemble prediction systems[END_REF] addresses the physical process associated to the upscale energy cascade from the grid scale to synoptic scales due to the excessive dissipation of energy in NWP models.

The combination of multiple model integrations of different analysis cycles generated from multiple initial conditions is another strategy to generate ensembles to capture the uncertainties associated both to the initial condition and to each model [START_REF] Hou | Objetive verification of the SAMEX'98 ensemble forecast[END_REF][START_REF] Palmer | Development of a European multimodel ensemble system for seasonal to inter-annual prediction (DEMETER)[END_REF]. Taking several global models as initial conditions provides better performance than any single model system [START_REF] Kalnay | Forecasting forecast skill in the Southern Hemisphere[END_REF][START_REF] Wobus | Three years of operational prediction of forecast skill[END_REF][START_REF] Krishnamurti | Improved weather and seasonal climate forecast from multimodel superensemble[END_REF][START_REF] Evans | Joint medium range ensembles from the Met. Office and ECMWF systems[END_REF].

EPS techniques used by limited-area models

It should be noted that limited-area models (LAM) have horizontal and vertical boundaries whereas global models cover the entire Earth having only vertical boundaries. For LAM, largerdomain models supply the data for the horizontal boundary conditions. Lower boundary conditions are a function of surface physics parameterizations. The quality of LAM or local model predictions is greatly affected by the quality of forecasts produced by the model supplying the lateral boundary conditions. Errors in forecasts from larger-domain models will move into the LAM's forecast domain and can amplify. High-resolution limited-area models are constrained to limited areas due to high computational cost of running on such a fine mesh. Uncertainty (errors) similar to those in the model supplying boundary conditions can spread rapidly across the limited domain of the high-resolution model forecast. Lateral boundary conditions largely control the position and evolution of features that cover the entire forecast domain. In a high-resolution mesoscale model running over a limited area, the placement and timing of synoptic-scale features are determined almost completely by the synoptic-scale model supplying the boundary conditions.

Not only global model can be used in developing EPS but also LAM are involved in designing LAM EPS, normally for the short range and covering fine domains in order to resolve the internal processes of convection over local areas. Error sources in LAM EPS are basically the same as in global EPS but as it was aforementioned LAM require lateral boundary conditions that update the weather situation regularly throughout the integration. These lateral boundary conditions introduce a main source of uncertainty in LAM EPS. Both LBCs and ICs contribute to the spread and skill of the system [START_REF] Clark | A comparison of precipitation forecast skill between small convection-allowing and large convection-parameterizing ensembles[END_REF].

All techniques discussed so far can be applied to generate LAM EPS but a common methodology is downscaling of global EPS. This approach consists of using the selected global ensemble members, which are previously chosen by clustering, as ICs and LBCs for a LAM EPS. Perturbations generated from the global EPS are usually effective only for the medium range and large scales. Therefore, this method is not suitable for short-range ensemble forecasting.

Another approach for sampling the LBC forecast error source is the Multi-Boundary technique in which several different global models supply LBCs to feed the limited-area model. The methodology based on the use of multiple-area models and multiple ICs coming from several global models at a time and combined with advanced statistical post-processing techniques was tested at the NCEP (Hamill and[START_REF] Hamill | Verification of ETA-RSM short-range ensemble forecast[END_REF]1998;[START_REF] Stensrud | Using ensembles for shortrange forecasting[END_REF]Du andTracton, 2001, Wandishin et al., 2001) during the Storm and Mesoscale Ensemble Experiment (SAMEX; [START_REF] Hou | Objetive verification of the SAMEX'98 ensemble forecast[END_REF]. Such probabilistic forecasts were also generated over the Pacific Northwest Coast [START_REF] Grimit | Initial results of a mesoscale short-range ensemble forescasting system over the Pacific Northwest[END_REF], over the Northeast Coast of the United States [START_REF] Jones | Evaluation of a mesoscale short-range ensemble forecast system over the Northeast United States[END_REF] and over a broad area covering most of the North-Atlantic Ocean, Europe, Northern Africa and the Mediterranean Sea by the short-range EPS from the Spanish Agency of Meteorology (AEMET; [START_REF] García-Moya | Predictability of short-range forecasting: a multi-model approach[END_REF].

Distinguishable and undistinguishable ensemble members

Depending on how the ensemble prediction systems are built, the ensemble members are either distinguishable (we can clearly identify each member or at least some of them) or indistinguishable (when the origin of the given member cannot be identified).

Most of the currently used ensemble prediction systems incorporate ensembles where at least some members are statistically indistinguishable. Such ensemble systems are usually producing initial conditions based on algorithms, which are able to find the fastest growing perturbations indicating the directions of the largest uncertainties (for instance, singular vectors computations [START_REF] Buizza | The singular vectors structure of the atmospheric general circulation[END_REF] or search for breeding vectors [START_REF] Toth | Ensemble forecasting at NCEP: The breeding method[END_REF]). In most cases, these initial perturbations are further enriched by perturbations simulating model uncertainties as well. In such cases, one usually has a control member (the one without any perturbation) and the remaining ensemble members are forming one or two exchangeable groups.

Usually, the distinguishable EPS systems are the multi-model, multi-analysis ensemble systems, where each ensemble member can be identified and tracked.

This distinguishable/undistinguishable feature has consequences in the way and utility of the statistical calibration of the raw ensemble system output (see Section 4.5, Deliverable 4.1).

Description of Ensemble Prediction Systems used in PreFlexMS

ECMWF Ensemble-Atmospheric Model

The European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System comprises both the 51-member ensemble (ENS, (Hágel, 2010)) and a single run highresolution forecast (HRES) which works at a horizontal resolution of 9 km (since spring 2016) and provides the ECMWF's most sophisticated and computationally demanding forecasts of future weather states at prediction horizons up to ten days ahead. Outputs from the 51member ECMWF ensemble are used in PreFlexMS project. The ENS configuration is shown in Fig. 10 Figure 10: The ECMWF Ensemble-Atmospheric Model

AEMET gSREPS

The configuration of the 20-member Spanish Meteorological Agency (AEMET) ensemble, called gamma Short Range Ensemble Prediction System (gSREPS) is shown in Fig. 11. AROME is a spectral, compressible non-hydrostatic limited-area model with a turbulent kinetic energy (TKE-based 1D) turbulent scheme, a bulk microphysics scheme with five 3D advected water species (cloud liquid water and ice, precipitating rain, snow and graupel), a subgrid shallow convection scheme, a detailed surface scheme (with tiles for soil, vegetation, lakes, towns, sea, sea ice and snow layer), and a simplified version of the ECMWF radiation scheme.

The AROME model and its data assimilation are extensively documented in [START_REF] Seity | The AROME-France convective-scale operational model[END_REF][START_REF] Seity | The AROME-France convective-scale operational model[END_REF].

ALARO model has been designed specifically to be run at convection-permitting resolutions.

The key concept behind this model lies in the precipitation and cloud scheme called modular multiscale microphysics and transport (3 MT), developed by [START_REF] Gerard | Evolution of a sub-grid deep convection parametrization in a limited area model with increasing resolution[END_REF], [START_REF] Gerard | An integrated package for sub-grid convection, clouds and precipitation compatible with the meso-gamma scales[END_REF] and [START_REF] Gerard | Cloud and precipitation parameterization in a Meso-Gamma-Scale operational weather prediction model[END_REF]. The ALARO model utilized the ACRANEB scheme for radiation [START_REF] Ritter | A comprehensive radiation scheme for numerical weather prediction models with potential application in climate simulations[END_REF], a semi-Lagrangian horizontal diffusion scheme called SLHD [START_REF] Váňa | Semi-Lagrangian advection scheme with controlled damping: An alternative to non-linear horizontal diffusion in a numerical weather prediction model[END_REF], some pseudo-prognostic turbulent kinetic energy (TKE) scheme (pTKE, i.e. a Louisetype scheme for stability dependencies, but with memory, advection and auto-diffusion of the overall intensity of turbulence) and statistical sedimentation scheme for precipitation within a prognostic-type scheme for microphysics [START_REF] Geleyn | A statistical approach for sedimentation inside a microphysical precipitation scheme[END_REF]. The configuration of ALARO with these physics runs operationally of a number of countries of the ALADIN and HIRLAM Consortia for the National NWP Applications since 2008.

The equation set for WRF-ARW is fully compressible, Eulerian and non-hydrostatic with a runtime hydrostatic option. It is conservative for scalar variables. The model uses terrainfollowing, hydrostatic-pressure vertical coordinate with the top of the model being a constant pressure surface. The horizontal grid is the Arakawa-C grid. The time integration scheme in the model uses the third-order Runge-Kutta scheme, and the spatial discretization employs 2nd to 6th order schemes. The model supports both idealized and real-data applications with various lateral boundary condition options. The model also supports one-way, two-way and moving nest options. It runs on single-processor, shared-and distributed-memory computers. The WRF-ARW model is fully documented in [START_REF] Skamarock | A Description of the Advanced Research WRF Version 3[END_REF].

The Non-hydrostatic Multi-Scale Model on the B grid (NMMB) core of the NOAA Enviromental Modeling System (NEMS) was developed by the National Oceanic and Atmospheric Adminstration (NOAA) National Center for Environmental Prediction (NCEP). The NMMB is designed to be a flexible, state-of-the-art atmospheric simulation system that is portable and efficient on available parallel computing platforms. NEMS-NMMB is a fully compressible, nonhydrostatic model with a hydrostatic option (Janjic, 2003a, Janjic and[START_REF] Janjic | Scientific documentation of the NCEP nonhydrostatic multiscale model on the B grid (NMMB). Part 1 Dynamics[END_REF] and hybrid (sigma-pressure) vertical coordinates on an Arakawa B-grid. It has a forward-backward scheme for horizontally propagating fast waves, implicit scheme for vertically propagating sound waves, Adams-Bashforth Scheme for horizontal advection, and Crank-Nicholson scheme for vertical advection. Full physics options for land-surface, planetary boundary layer, gravity wave drag, atmospheric and surface radiation, microphysics, and cumulus convection are available. It also supports one-way and two-way nesting with multiple nests. The NEMS-NMMB model is fully documented in [START_REF] Janjic | Scientific documentation of the NCEP nonhydrostatic multiscale model on the B grid (NMMB). Part 1 Dynamics[END_REF].

Uncertainty representation

In probability weather forecasting, uncertainty is represented by means of the Probability Density Function (PDF). Let us consider a random variable x that we do not know anything about its nature. The question is whether we can infer something from that variable. If we take n different values of x that belong to the same population, we can obtain an approximation of the PDF of the random variable x when constructing the histogram of these values.

As an example, we could think of the variable x as the mean monthly temperature of April at a surface observation station. Then, the population corresponding to the variable x would be the mean monthly temperatures of April at that station. If we restrict the study period from 1981 to 2010, the n=30 values of x would form the sample space.

The PDF gives information about the behavior of the random variable x. Taking the normal or Gaussian PDF of x, the analytical formula is represented as follows:

𝑷𝑷𝑷𝑷𝑷𝑷(𝒙𝒙) = 𝟏𝟏 � 𝟐𝟐𝟐𝟐𝝈𝝈 𝟐𝟐 𝒆𝒆 (𝒛𝒛-𝝁𝝁) 𝟐𝟐 𝟐𝟐𝝈𝝈 𝟐𝟐 ( 1 )
Where σ is the standard deviation and μ is the mean.

Plotting the PDF of the random variable x according to the Equation (1) as it is shown in Figure 12, it can be noticed there is a value of μ around which all the random values of x are distributed symmetrically.

Likewise, σ is a measure of the standard deviation of x from its mean. We can think of σ as the mean error or uncertainty we would have if we approximated any possible values of x by μ.

Summarizing, the PDF gives a depiction of all possible values of the random variable x and their associated probabilities of occurrence, resulting this approach in a quantitative way to represent the uncertainty of a random variable.

From the Numerical Weather Prediction (NWP) perspective is computationally unfeasible to integrate the Liouville Equation (also referred as Fokker-Plank Equation) that describes the time evolution of a PDF when random processes are included to account for model error. A practical approximation to resolve this computational problem is to use an Ensemble Prediction System (EPS).

EPS tries to estimate the uncertainty of the forecast by discretizing the forecast PDF for each model variable at each grid point in N values corresponding to N ensemble members. As an example, Fig. 13 shows the forecasted PDF 2m-temperature at forecast length H+60 by the AEMET-SREPS [START_REF] García-Moya | Predictability of short-range forecasting: a multi-model approach[END_REF] for the closest grid point to Sevilla (Spain). This ensemble was formed by 25 members, but for this particular case, there was only one ensemble member that did not integrate properly, so N=24. It can be noticed the more ensemble members are the higher is the resolution of the PDF. A simplified approach to represent the uncertainty of the forecast from EPS is the spread [START_REF] Toth | Ensemble forecasting at NCEP: The breeding method[END_REF]) measured as the standard deviation σ Equation (2) of the PDF. The standard deviation quantifies how much the ensemble members deviate from the mean, on average, and it is often used as a measure of the spread (Wilks, 2006).

𝝈𝝈 = � 𝟏𝟏 𝑵𝑵 ∑ (𝒇𝒇 𝒊𝒊 -𝒆𝒆𝒆𝒆) 𝟐𝟐 𝑵𝑵 𝒊𝒊=𝟏𝟏 ( 2 )
Where f i is the forecasted variable by ensemble member i on each grid point and em is the ensemble mean, e.g. the mean of the N forecasts. In the aforementioned case study of 2mtemperature forecast, em and the spread are 32.3°C and 1.5°C, respectively. The spread measured, as standard deviation is an estimation of the error of the deterministic forecast i so that the higher the spread is the higher uncertainty is associated to the forecast.

Ensembles are composed of individual members that are deterministic predictions and allow providing individual deterministic information about the forecast [START_REF] García-Moya | Predictability of short-range forecasting: a multi-model approach[END_REF].

This information supports the probabilistic interpretation of the EPS when it is considered as an intrinsically probabilistic prediction system.

The ensemble mean (em) forecast is a simple but effective product. The averaging serves as a filter to reduce or remove atmospheric features that varies amongst the members and is therefore likely to be regarded as less predictable at the time. Such non-predictable features are effectively removed from the em. Significant high-impact events are often weakened or absent in the em. Use of probabilities is therefore essential in conjunction with the em.

Ensemble mean is most suited to parameters like temperature and pressure, which usually have a rather symmetric Gaussian distribution. It is less suitable for wind speed and precipitation because of their skewed distributions. For these parameters, the median might be more useful. It is defined as the value of the middle ensemble member, if the members are ordered according to rising (ranked) values. Due to the anti-symmetry of the initial perturbations, the em is very similar to the Control (or HRES) in the short range.

Ensemble mean tends to weaken gradients: all members might forecast an intense lowpressure system with 15-20 m/s winds in different positions. These differences in position lead to a rather shallow low in the em, which gives the impression of weak average winds.

The ensemble spread is a measure of the difference between the members and is represented by the standard deviation with respect to the em. On average, small spread indicates high a priori forecast accuracy and large spread low a priori forecast accuracy. The ensemble spread is flow-dependent and varies for different parameters. It usually increases with the forecast range, but there can be cases when the spread is larger at shorter forecast ranges than at longer. This might happen when the first days are characterized by strong synoptic systems with complex structures but are followed by large-scales 'fair weather' high-pressure systems.

The spread around the em as a measure of a priori accuracy applies only to the em forecast error, not to the median, the Control or the HRES, even if they happen to lay mid-range within the ensemble.

The ensemble spread should reflect the diversity of all possible outcomes, in particular when the deterministic forecasts are "jumpy", which might indicate that different weather developments are possible.

Generally, whether the ensemble spread is small or large, the em (or median) will, beyond the short range, exhibit higher accuracy than the Control (and high-resolution forecast); this is particularly true for "dry" parameters, such as MSLP and temperature. With increasing spread, the forecast information will depend more heavily on the probabilities; this is particularly true for "wet" parameters, such as precipitation and cloud amounts. The em will also display a higher degree of day-to-day consistency.

Although em and, similarly, averages of forecasts from the same or different models provide more accurate and considerably less "jumpy" forecasts than deterministic forecasts, meteorologists are somewhat apprehensive about using them. This reluctance derives mainly from three reasons:

• Ensemble averages do not constitute genuine, dynamically three-dimensional representations of the atmosphere. • Ensemble averages are less able to represent extreme or anomalous weather events.

• Ensemble averages might lead to inconsistencies between different parameters.

To avoid over-interpreting the em, it should preferably be presented together with a measure of the ensemble spread or event probabilities; these will convey an impression complementary to the em.

The most consistent way to convey forecast uncertainty information is by the probability of the occurrence of an event. The event can be general or user-specific representing the exceedance of a threshold. The event threshold often corresponds to the point at which the user has to take some action to mitigate for the potential damage of a significant weather event.

Probabilities can be instantaneous, such as 10m probabilities. They can also be calculated over a time interval, for instance precipitation, because the values are themselves originally computed as values accumulated over some time interval.

Probabilities give no indication of the physical nature of the uncertainty. A 25% probability of precipitation > 5 mm/24h might be related to a showery regime or to the uncertainty of the arrival of a frontal rain band. A 25% risk forecast for temperatures < 0ºC might be related to the possible early morning clearing of low cloud cover or the possible arrival of artic air. Moreover, probability forecasts cannot be linearly extrapolated into the future. Thus, if an event was assigned a 10% probability in the forecast two days ago, 20% yesterday's forecast and 30% today's, there is no reason that it will necessarily further increase in tomorrow's forecast; it could equally well remain at its current level or decrease.

Data sent from AEMET to CENER

Parameters

The ensemble data that AEMET will provide to CENER are the same parameters as in the HRES case, see section 1.4.1.

Temporal availability

The ECMWF-EPS forecasts that AEMET will send to CENER, as in the case of HRES data (Section 1.4.2), is 3-hourly data up to H+72 h runs at 00 and 12 UTC. Outputs from the ECMWF-EPS will be available approximately 9 h after the nominal time (Table 10).

AEMET is currently developing a Meso-scale EPS (MEPS) based on a multi-model approach (Harmonie AROME, Harmonie ALARO, WRF-ARW and NMMB), called gSREPS, with 2.5 km spatial resolution and covering the Iberian Peninsula and Northern Africa for 36 hour forecasts. It will have 20 members and be updated 6-hourly (Table 10).

Data format

The ensemble data that AEMET will provide to CENER will have the same format as described in Section 1.4.3.

Forecasts provided by CENER to partners for R&D

Parameters

Two different sources of probabilistic forecast will be available in the framework of this project. One hand, the EPS (Ensemble Prediction System) of the ECMWF that provides fifty one different meteorological forecasts and, on the other hand the gSREPS system of AEMET will generate 20 different forecasts. So, CENER will provide the same number of DNI forecasts like members delivered by the respective EPS.

Temporal availability

As in the case of deterministic forecast, the temporal resolution of the DNI predictions will be increased up to achieving 15-minute frequency. Related to the schedule of delivery of probabilistic forecast in the operative situation, the estimation of times is compiled in Table 11.

Data format

The data format will be NetCDF.

Table 12 contains the information of each NetCDF data section: Name, data format and a brief description of the data value. The probabilistic forecasts is delivery by mean of all the individual members of the ensemble forecast.

Name Format Description

Date aaaammddhh

The date when the forecast has been made (UTC). It contains four digits indicating the year (aaaa), two digits indicating the month (mm), two digits indicating the day (dd) and two digits containing the hour (hh).

DatePred

aaaammddhhMM The predicted date (UTC). It contains four digits indicating the year (aaaa), two digits indicating the month (mm), two digits indicating the day (dd), two digits containing the hour (hh) and two digits indicating the minute (MM)

Step

Float

The horizon of forecast. That is, the step ahead which the prediction is made.

Lat

DNI_M1

Float

The first member of the ensemble forecast. Average DNI as power (W/m 2 ) over the time interval.

⁞ ⁞ ⁞

DNI_Mx

Float

The n-th member of the ensemble. (W/m 2 )

T2M_M1

Float

The first member of the ensemble forecast. Average temperature (°C) at 2 m height over the time interval.

⁞ ⁞ ⁞

T2M_Mx

Float

The n-th member of the ensemble.

T10M_M1

Float

The first member of the ensemble forecast. Average temperature (°C) at 10 m height over the time interval.

⁞ ⁞ ⁞

T10M_Mx

Float

The n-th member of the ensemble.

T200M_M1

Float

The first member of the ensemble forecast. Average temperature (°C) at 200 m height over the time interval.

⁞ ⁞ ⁞

T200M_Mx

Float

The n-th member of the ensemble.

VEL10_M1

Float

The first member of the ensemble forecast. Average wind speed (m/s) in 10 m height over the last 10 minutes time before output time step.

⁞ ⁞ ⁞

VEL10_Mx

Float

The n-th member of the ensemble.

VEL200_M1

Float

The first member of the ensemble forecast. Average wind speed (m/s) in 200 m height over the last 10 minutes time before output time step.

⁞ ⁞ ⁞

VEL200_Mx

Float

The n-th member of the ensemble.

DIR10_M1

Float

The first member of the ensemble forecast. Average wind direction (grades, 0º=North direction, clock-wise) in 10 m height over the last 10 minutes time before output time step.

⁞ ⁞ ⁞

DIR10_Mx

Float

The n-th member of the ensemble.

DIR200_M1

Float

The first member of the ensemble forecast. Average wind direction (grades, 0º=North direction, clock-wise) in 200 m height over the last 10 minutes time before output time step.

⁞ ⁞ ⁞

DIR200_Mx

Float

The n-th member of the ensemble.

Note that the error code for any variable is -999. for float and -999 for integer variables.

Forecasts provided by CENER during the demonstration phase

The format and information delivered will be the same when the aim is the demo activities or the R&D ones. The main difference is that in case of demo, periodic deliveries will be made coinciding with each new NWPM output availability, as is described in Table 11, meanwhile in case of R&D activities the delivery will be formed by one historic of forecasts. This historic will contain a simulation of operative probabilistic forecast deliveries with the same temporal resolution and variables that those of the demo case.

Conclusions

In this report we have described the principles from both deterministic and probabilistic weather forecasting perspectives providing an overview of the numerical weather prediction models used for solar radiation forecasting in PreFlexMS project. The forecasts and data formats have been also established.

Figure 1 :

 1 Figure 1: Assimilation and forecast cycle of a numerical model. The observations and the first-guess field are combined to obtain the analysis.

Figure 2 :

 2 Figure 2: Scheme of the models described in the text.

Figure 3 :

 3 Figure 3: Blue box: HIRLAM model operational domains at AEMET since February 2005. Red boxes: Experimental HARMONIE geographical domain. Figure obtained from Navascues et al., 2013.

Figure 4 :

 4 Figure 4: Time schedule for Harmonie using the normal cycle (UTC). ECMWF/IFS is used for boundary conditions (BC).

Figure 5 :

 5 Figure 5: Time schedule for RUC1 (UTC).

Figure 6 :

 6 Figure 6: Horizontal area covered by the HARMONIE data delivered from AEMET to CENER. The location of Badajoz and Évora stations is included in the figure.

  Futhermore, this variable is obtained by the post-processing of the Direct Model Output (DMO) from AROME/HARMONIE or ECMWF (European Centre for Medium-Range Weather Forecasts) forecasts. The post process is based on machine learning and uses the local information offered by the ground measurements available in the emplacement. So, this will adapt the direct model output of ECMWF or HARMONIE to local and reduce systematic biases. This post-process is based in the implementation of a module forecasting type of sky conditions (clear or cloudy) at a given time step by Random Forest technique. Once determined the type of sky conditions, a clear sky model or a Machine-Learning-based irradiance model will be applied for clear and cloud conditions, respectively.

Figure 7 :

 7 Figure 7: Measured (red) and DP (blue) generated 1-min DNI at TAM, for different day types. BSRN station at Tamanrasset, Algeria.

  Float Latitude of the site. (North positive) Lon Float Longitude of the site. (East positive) DNI Float The Direct Normal Irradiance predicted by the model. Average DNI as power (W/m2.) over the time interval P10 Float A measure of DNI forecast uncertainty: probability of exceedance 10 calculated on the differences between historical measurements and datasets as a function of solar elevation and beam clearness index P25 Float A measure of DNI forecast uncertainty: probability of exceedance 25 calculated on the differences between historical measurements and datasets as a function of solar elevation and beam clearness index P75 Float A measure of DNI forecast uncertainty: probability of exceedance 75 calculated on the differences between historical measurements and datasets as a function of solar elevation and beam clearness index P90 Float A measure of DNI forecast uncertainty: probability of exceedance 90 calculated on the differences between historical measurements and datasets as a function of solar elevation and beam clearness index T2M Float Average 2 meter temperature in the time interval. (ºC) T10M Float Average 10 meter temperature in the time interval. (ºC) T200M Float Average 200 meter temperature in the time interval. (ºC) VEL10 Float 10 meter wind speed. Averaged for the last 10 minutes before the output time step. (m/s) VEL200 Float 200 meter wind speed. Averaged for the last 10 minutes before output time step. (m/s) DIR10 Float 10 meter wind direction. (grades, 0º=North direction, clock-wise) DIR200 Float 200 meter wind direction. (grades, 0º=North direction, clock-wise)

Figure 8 :

 8 Figure 8: Singular vector approach.

Figure 11 :

 11 Figure 11: AEMET-γ-SREPS.

Figure 12 :

 12 Figure 12: Gaussian PDF (μ=0, σ=1).

Figure 13 :

 13 Figure 13: Histogram of 2m-temperarute forecasted at H+60 by AEMET-SREPS at the closest grid point to Sevilla (Spain). Valid time: 30 th June 2011 at 12:00 UTC.

Float

Table 1 : Surface parameters from HARMONIE. Parameter definition

 1

		Parameter
		Identifier (indicatorOfPara	Level	Inst / Acc	Units
		meter grib key)
	Surface solar radiation (SW down global)	117	0	Accumulated	Jm -2
	Surface direct solar flux (Surface parallel solar flux)	116	0	Accumulated	Jm -2
	Surface Pressure	1	Above ground	Instantaneous	Pa
	Mean Sea Level Pressure	1	Above mean sea level	Instantaneous	Pa
	Total Cloud Cover	71	0	Instantaneous	%
	Wind u-component	33	10 m	Instantaneous	ms -1
	Wind v-component	34	10 m	Instantaneous	ms -1
	Temperature	11	2 m	Instantaneous	K
	Low Cloud Cover	73	0	Instantaneous	[0-1]
	Medium Cloud Cover	74	0	Instantaneous	[0-1]
	High Cloud Cover	75	0	Instantaneous	[0-1]
	Relative Humidity	52	2 m	Instantaneous	[0-1]

Table 3 : Model level parameters from HARMONIE. Parameter definition

 3

		Parameter
		Identifier (indicatorOfPara	Model level	Inst / Acc	Units
		meter grib key)
	200 metre wind u-component	33	aprox. level 60	Instantaneous	ms -1
	200 metre Wind u-component	34	aprox. level 60	Instantaneous	ms -1
	10 metre Temperature	11	aprox. level 65	Instantaneous	K
	200 metre Temperature	11	aprox. level 60	Instantaneous	K

Table 3 : Parameters from the ECMWF. Parameter definition Parameter Identifier (paramId grib key) Level Inst / Acc Units

 3

	Surface Solar Radiation Downwards	169	0	Accumulated	Jm -2
	Total Sky direct Solar Radiation at Surface	228021	0	Accumulated	Jm -2
	Surface Pressure	134	Above ground	Instantaneous	Pa
	Mean Sea Level Pressure	151	Above mean sea level Instantaneous	Pa
	Total Cloud Cover	164	0	Instantaneous	(0-1)
	10 metre U Wind Component	165	10 m	Instantaneous	ms -1
	10 metre V Wind Component	166	10 m	Instantaneous	ms -1
	2 metre Temperature	167	2 m	Instantaneous	K

Table 5 : Model level parameters from the ECMWF model.

 5

		Parameter
	Parameter definition	Identifier	Model level	Inst / Acc	Units
		(paramId grib key)
	200 metre U Wind Component	131	aprox. level 130	Instantaneous	ms -1
	200 metre V Wind Component	132	aprox. level 130	Instantaneous	ms -1
	10 metre Temperature	130	aprox. level 137	Instantaneous	K
	200 metre Temperature	130	aprox. level 130	Instantaneous	K

Table 5 .

 5 At

main cycles, 00, 06, 12 and 18 UTC, the model will provide data up to H+48h while at the 03, 09, 15 and 21 UTC it will provide H+6 or H+12 depending on availability, although the final decision about the forecast length of intermediate runs is not yet taken. The output is available about 3 hours after the nominal time i.e. the output of the 00Z is available at about 03Z, the output of the 03Z at 06Z, etc. The schedule is presented in Figure

4

; for simplicity, only two of the daily runs are shown. If the rapid update cycle (RUC1) is available, the model will be run every hour (being 00, 03, 06, 09, 12, 15, 18 and 21 UTC normal cycles, and the rest short cycles).

Table 5 : High resolution operational data that will be provided from AEMET to CENER.

 5

	Model	Run Time (UTC)	Forecast Range (h) Temporal Resolution
	HARMONIE	00-03-06-09-12-15-18-21	Up to 48	15 min
	ECMWF	00-12	72	3 h

Table 6 : CENER data availability for the demonstration phase.

 6

			Delivery time
	NWPM	Runs (UTC)	AEMET to CENER (Processing	CENER (Processing & Delivery)	Remaining horizon provided by CENER (h)
			& Delivery)
	AROME / HARMONIE	00-06-12-18	3h	1h	44
	ECMWF	00-12	7h	1h

Table 7 : Data format description. Name Format Description Date yyyymmddhh

 7 The date (UTC) when the forecast has been made. It contains four digits indicating the year (yyyy), two digits indicating the month (mm), two digits indicating the day (dd) and two digits containing the hour (hh).

Table 9 : gSREPS members with corresponding NWP models and BCs.

 9

	Member #	NWP Model	Bounday Conditions
	01	HAR / AROME	ECMWF -IFS
	02	HAR / ALARO	ECMWF -IFS
	03	WRF -ARW	ECMWF -IFS
	04	NMMB	ECMWF -IFS
	05	HAR / AROME	NCEP -GFS
	06	HAR / ALARO	NCEP -GFS
	07	WRF -ARW	NCEP -GFS
	08	NMMB	NCEP -GFS
	09	HAR / AROME	MF -ARPEGE
	10	HAR / ALARO	MF -ARPEGE
	11	WRF -ARW	MF -ARPEGE
	12	NMMB	MF -ARPEGE
	13	HAR / AROME	CMC -GEM
	14	HAR / ALARO	CMC -GEM
	15	WRF -ARW	CMC -GEM
	16	NMMB	CMC -GEM
	17	HAR / AROME	JMA -GSM
	18	HAR / ALARO	JMA -GSM
	19	WRF -ARW	JMA -GSM
	20	NMMB	JMA -GSM

Table 10 : Ensemble operational data that will be provided from AEMET to CENER.

 10

	Model	Run Time (UTC)	Forecast Range (h)	Temporal Resolution
	gSREPS	00-06-12-18	36	1 h
	ECMWF	00-12	72	3 h

Table 11 : CENER data availability for the demonstration phase.

 11

			Processing & Delivery
	NWPM	Runs (UTC)	time AEMET to CENER	CENER	Remaining horizon provided by CENER (h)	Members of EPS
	ECMWF	00-12	9h	1h	62	50
	gSREPS	00-06-12-18	5h	1h	32	20

Table 12 : Data format description.

 12

D4.3-Weather Forecast Requirements and Evaluation Methods H2020-PreFlexMS/ Grant no. 654984

Hágel & Horányi (2007). The ARPEGE/ALADIN limited area ensemble prediction system: the impact of global targeted singular vectors. MeteorologischeZeitschrift, 16, Number 6, December 2007, pp. 653-663.

DCH direction changes in DNI DHI diffuse hemispherical irradiation DLR German Aerospace Center DMO Direct Model Output DNI direct normal irradiation DNIcast Project acronym www.dnicast-project.net DRIBU buoys observations DRIFTER observations from drifting buoys ECMWF European Centre for Medium-Range Weather Forecast ECMWF/EPS ECMWF/Ensemble Prediction System ECMWF/IFS ECMWF/Integrated Forecast System EDA Ensemble Data Assimilation ELR extended logistic regression em ensemble mean