Forest-based Methods and Ensemble Model Output Statistics for Rainfall Ensemble Forecasting

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Renewable energy growth

In the recent years, the energy transition has been on the forefront of political and societal issues, mainly due to the increasing awareness of the need to maintain climate change within acceptable bounds. This has led many countries to encourage the use of renewable energy. Since 2008, the European Union (EU) targets 20% of renewable energy contribution to the total energy mix by 2020, and 27% by 2030. Owing to a well-established technology and the ever stronger push towards replacing fossil fuels with clean renewable power, wind energy has seen a dramatic growth in the recent years. As an illustration of this sharp increase, the newly installed wind capacity in the world in 2016 has been 55GW, corresponding to an increase of 12.6% in the total installed capacity (Global Wind Energy Council (GWEC, 2016)). In 10 years, the total worldwide installed capacity has almost been multiplied by 7, going from 74GW installed in 2006 to almost 500GW in 2016 (Figure 1.1). In the EU, the total installed wind power capacity has grown from 13 GW in 2000 to 142 GW in 2015 (EWEA, 2016). The actual share in the nal consumption met by wind energy in the EU was 11.4% in 2015 (EWEA, 2016). The number of wind farms increases each year and feeds the electrical network with a larger amount of energy. In 2016, France has seen its highest capacity growth rate ever recorded. This sharp increase of connected wind power has for instance allowed the network to receive 8.6 GWh from wind power plants, on November 20th at night, corresponding to 17.9% of the energy produced at this time (RTE, 2016a).
The increase of wind and PV power raises the issue of their natural varability. For producers, the management of price uctuations, the optimisation of operation costs, and of the wind turbines’ maintenance are typical concerns. For transmis-sion system operators (TSOs), the exact balance between electricity supply and demand at every time step is becoming more and more challenging as the number of wind farms and PV power plants connected to the electrical network increases. Naturally variable renewable energy penetration is thus a challenging issue, because the predictability of this type of energy is related to very complex processes of the atmospheric circulation. The atmospheric circulation displays variability at very dif-ferent spatial and temporal scales, and its chaotic nature might limit or slow down the penetration of such energy production means.

Variability and its implications

Atmospheric variability

The Earth is often described as a thermodynamic system in equilibrium. Motions in the atmosphere are mainly initiated by solar radiation heating the atmosphere. The amount of energy from the sun is much larger in equatorial regions than in polar regions. Thermal gradient generates heat uxes crossing latitudes by means of three cells constrained by the Coriolis force, namely the Hadley cell (in tropical regions), the Ferrel cell (at midlatitude) and the polar cell (in polar regions). This circulation is known as the global atmospheric circulation (Figure 1.2).
Figure 1.2: Schematic of the global atmospheric circulation. The motions in the vertical cross section represent the circulation averaged in time and along parallels.
The atmosphere is a complex system and the atmospheric circulation involves motions on a wide range of space and time scales, interacting to produce variability on scales from seconds to decades. Figure 1.3 shows the typical spatial scales of the atmospheric circulation and the corresponding time scale as well as examples of phenomena associated with them.
In the vertical, the atmosphere can be divided into 4 layers depending on the sign of the vertical pressure gradient. The layer in which we live, which touches the surface and has temperature decreasing with height is the troposphere. It typically extends to 10km altitude at midlatitudes. It is heated from below, by the absorption of solar radiation at the surface. More precisely, the lowest part of the troposphere is the boundary layer (typically 1km thick). It is in contact with the surface and directly in uenced by exchanges of heat, momentum. The rest of the troposphere is called the free troposphere.
In the free troposphere (typically above 1km) and in mid or high latitudes, the ow is quasi two-dimensional, the synoptic scale (about a thousand km) is predominant, and the wind is mainly geostrophic, i.e. equilibrium between the Coriolis and the pressure forces. At those altitudes, the circulation patterns extend to a very large spatial scale. The geostrophic balance results in wind parallel to the isobars, explaining cyclonic (around low pressure) and anticyclonic (around high pressure) circulations.
In the lowest layer of the atmosphere, called the boundary layer (Figure 1.4) (typ-ically extended to 1km in vertical), the ow is three dimensional and vertical mixing is usually strong. Turbulent eddies with dimensions at most comparable to the boundary layer height are predominant, so that the wind displays rapid variations from seconds to minutes. Those uctuations are strongly linked to the interaction of the ow with the surface. Within the boundary layer, meteorologists distinguish the surface layer (typically up to 100m) where surface friction induces high vertical shear of the ow and thus generates turbulence. The vertical pro le of the wind in these parts of the atmosphere is logarithmic, and depends on the surface roughness and friction velocity which describes the turbulence of the ow.
While the previous paragraphs emphasize the contrast between the synoptic scale in the free troposphere and the short, turbulent scales of the boundary layer, there are also motions in uenced by the surface at intermediate scales (from few km to a few hundreds). Larger scale ow also interacts with surface orography which drives the dynamics of the near surface wind speed by de ecting, accelerating the ow, or even giving birth to wakes and orographic waves breaking. The ow impinging on a hill may pass over or may split around, depending on the ow mean velocity, and the height of the obstacle (Smith, 1989). If a valley is formed by two reliefs the ow channelled in between can be accelerated and give birth to sustained strong winds, as it is the case in the south of France for the Mistral and Tramontane winds. In coastal areas, local thermal di erences between land and sea can generate sea breeze systems often driven by the diurnal cycle, which generates temperature gradients between a rapidly heating land surface and slowly heating ocean (Simpson, 1994).
In at areas, surface wind speed is induced by and varies with the large-scale ow. Systems such as fronts and cyclones can produce sustained strong winds. These systems are associated with jet streams induced by strong latitudinal thermic gradients (Figure 1.5). At midlatitude, the jet stream forms a barrier between polar cold air and warmer midlatitude air mass. It displays a seasonal variability and is usually stronger in winter, when thermal gradients are more important. It also displays spatial variability, with areas of stronger winds. These areas are usually related with the formation of precipitation systems such as lows, fronts and storms (Hall et al., 2015).
The jet stream state can be associated with weather regimes, which is a quite in-tuitive notion as they correspond to long periods of similar weather type. They can be de ned by the probability of occurrence, the persistence, or the quasi-stationary character of large scale atmospheric circulation patterns ((Michelangeli et al., 1995)). For instance, (Plaut and Simonnet, 2001), amongst others, discuss two of the usual European weather regimes, namely the Atlantic Ridge regime (AR) which induces westerlies over Western Europe and the Blocking regime (BL) which results in North-easterlies and is often associated with a cold spell over central and western Europe. Weather regimes come from the classi cation of large scale atmospheric circulation patterns obtained through dimension reduction techniques.
A typical example of such a pattern is the North Atlantic Oscillation (NAO) quanti ed by an index which measures the time-varying pressure di erence between the Islandic low and the Azores high pressure system. The strong pressure di er-ence between these locations forms the storm track which brings high precipitation systems and strong westerlies in Northern Europe (Trigo et al., 2002). When the NAO index is positive, the pressure gradient strengthens, so that the storm track is enhanced. Conversely, negative NAO index values correspond to a weaker pressure gradient. As a consequence, the interannual variability of the European weather is partly explained through the NAO index (Lau, 1988; Rogers, 1997; Trigo et al., 2002; Scaife et al., 2014). A more famous large scale pattern is the so called El Nino Southern Oscillation (ENSO) which comes from the displacement of the Walker cell in the paci c region. The displacement of this cell has strong impacts on the oceanic circulation in the paci c tropical region (Rasmusson and Carpenter, 1982). This os-cillation has been shown to in uence the atmospheric circulation at the global scale (Cassou, 2008), but mainly in tropical regions (Luo et al., 2005).

Implication for energy management

Assessing wind energy production from surface wind speed is not straightforward and demands a lot of considerations. First, measurements are usually available at 10m which is a level of reference in meteorology. Wind turbines harvest wind at heights ranging from 50m to 140m (Hernandez et al., 2017), so that vertical extrapolation of the surface wind speed at the hub height is often necessary to evaluate the power production. The vertical extrapolation of wind speed is based on surface boundary layer theory and depends on many parameters so that it always induces uncertainties (Kubik et al., 2011). Second, assessing the resource for prospection purposes also should be based on a long time series of observations typically of the range of 30 years, which corresponds to the climatological scale. Indeed, climatology consists in a long time series that gathers the interannual variability modes of the variable of interest. Unfortunately, continuous and homogeneous observations are usually not available on such long time periods, so that numerical modelling and downscaling is needed to obtain a modelled long time series representative of a site or a region. The wind speed obtained is very often tted with the theoretical Weibull distribution which has over the years become a standard in the wind energy industry. This distribution is based on two parameters only and is thus easy to t, which is one of the main reasons of its widespread use. It shows good results in many regions, but its use has been challenged as it is not always the best theoretical distribution to represent observations, especially in mountainous regions (Drobinski et al., 2015; Jourdier and Drobinski, 2017; Earl et al., 2013). Finally, to obtain wind energy production, the power curve of a given turbine is applied to the wind speed distribution, which results in uncertainties. Indeed, in practice, the real power obtained from a turbine di ers from the one expected from the manufacturer’s power curve, for instance due to the variations of the air density or the varying intensity of turbulence.
If the assessment of the resource in advance for prospection purposes constitutes a domain in itself, the management of installed wind energy is also a large domain of interest. Indeed, energy transition from conventional production means as coal, gas, oil, and nuclear to mainly wind and solar energy constitutes a real change of paradigm. Wind and solar power production is naturally variable and hard to predict whereas conventional plants are much easier to control. The variability of the resource at di erent timescales raises many issues related to the economic viability of producers, the management of the supply and demand balance, but also to turbines maintenance planning, turbines safety, network safety etc. (Table 1.1).

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Strategies for forecasting wind energy

State of the art

Several forecasting problems in the wind energy sector can be related to di erent scales of the atmospheric variability (Table 1.1). Di erent strategies for accurately forecasting wind speed and power have been developed depending on these di erent spatio-temporal scales. These strategies can usually be classi ed into 2 categories :
Statistical methods based on time series analysis. These methods are often based on tting relations or learning algorithms that are able to reproduce from past observations and/or explanatory variables, the variable of interest at a given horizon. Many models exist from the simplest linear regression, or autoregressive model, to much more complex models such as arti cial neural networks (ANN).
Physical methods based on numerical models that solve the physical equations driving the atmospheric motions. Wind speed and components from numerical models allows to compute wind energy production from the power curve given by wind turbine suppliers.
At very short timescales (below 30 minutes), for the safety of the electricity network, energy is exchanged on the balancing market so that ’real time’ forecasts are needed (Table 1.1 & 1.2). Turbulence in the near surface boundary layer is then of great importance when trying to forecast very short-term wind power. Persistence is a classical benchmark method for very short-term forecasts as the autocorrelation of the wind can be strong at very short-term horizons. Several statistical methods have been studied and can, in some cases, over-perform the persistence (See for instance (Dowell and Pinson, 2016; Potter and Negnevitsky, 2006; Carpinone et al., 2015)). Nowcasting is a method based on high resolution Numerical Weather Prediction (NWP) models with real-time assimilation and time extrapolation of observations. It was historically used to follow heavy precipitation events in real-time. Some tools have been developed to apply this method to wind energy forecasts. It is however expensive in terms of computing resources so that statistical methods are usually preferred in the wind energy sector due to operational constraints.
At short timescales, wind energy producers must sell energy on the day-ahead and intra-day energy market, on which energy is sold at maximum a day ahead but can also be sold from 30 minutes to several hours ahead (Table 1.1 & 1.2). Short-term forecasts of wind speed and power are thus vital for wind energy producers to operate their wind farms and sell their production in an optimal way.
Many studies focus on the short-term prediction of wind speed. Most of them use purely statistical methods fed with past observations as in Sfetsos (2002) who compare Arti cial Neural Networks (ANN) methods with Autoregressive Integrated Moving Average (ARIMA) models from 1 hour to 1 day or Gomes and Castro (2012) who also develop ANN and Autoregressive Moving Average (ARMA) models but only at 1 hour horizon or Barbounis et al. (2006) who uses ANN to forecast wind speed at 3 days horizons with hourly resolution. NWP forecasts are also found useful at this timescale. NWP predictions can be used as such (Wagenbrenner et al., 2016; Sperandio et al., 2013) or can be post-processed using statistical models (Horvath et al., 2011; Giorgi et al., 2011).
At the turbine and farm level, forecasts of sudden changes (also called ramps) of the wind speed have long been a point of concern, not only for marketing purpose, but also for turbine safety. Ramp detection is also a large eld of research and can be addressed by purely statistical methods (Wytock and Kolter, 2013; Cui et al., 2015) or NWP forecasts (Bossavy et al., 2013).
At medium-term timescales (several days to maximum 10 days), forecasting methods have also been investigated in depth. Benchmarks have been provided within the ANEMOS project (Kariniotakis and Mayer, 2004; Marti et al., 2006) as well as within the International Energy Agency (IEA) task 36 (Mohrlen et al., 2018). Several methods, mainly based on NWP ensemble forecast outputs, have been pro-posed and analysed (Taylor and Buizza, 2002; Roulston et al., 2003; Taylor et al., 2009; Wan et al., 2014; Alessandrini et al., 2015; Taillardat et al., 2016). At these timescales, NWP prediction model outputs are much more widely used because of their ability to accurately forecast relatively large-scale systems for time horizons of half a day to weeks. Moreover, studies have dealt with the assessment of proba-bilistic forecasts (Pinson et al., 2007; Mohrlen and Bessa, 2018) and the way to use them in risk assessment and decision making frameworks (Pinson et al., 2009b).
On much longer timescales and with very di erent motivations, the impact of climate change on wind speeds has also been addressed (Sailor et al., 2008; Najac et al., 2009; Pryor and Barthelmie, 2010) in order to assess trends of wind energy production for prospection purposes (Table 1.1).

Toward seasonal prediction

Whereas both relatively short and very long timescales have been thoroughly stud-ied, the intermediate timescale going from a fortnight to the seasonal horizon is a research topic for which not so many studies exist. This timescale is of inter-est for anticipating maintenance operations, and to a lesser extent for market risk management. In particular, seasonal forecasting is becoming very important for Transmission System Operators (TSOs) as the proportion of intermittent resources in the energy mix increases.
Figure 1.6 shows for a scenario of wind energy penetration (Burtin and Silva, 2015) (60% of renewables, and 280GW of onshore wind power installed in Europe) the daily wind power production computed from 30 climatic years (i.e reanalyzed years from ERA-Interim reanalysis ((Dee et al., 2011), for which the atmosphere state is estimated numerically from observations). It displays a strong seasonal vari-ability as the average capacity factor is 30% in winter and 15% in summer. However, the spread of the production amongst these 30 years is the most problematic for net-work management. Indeed, from year to year, the average daily onshore wind power in winter can vary from less than 50GW to more than 150GW.
TSOs are responsible for balancing supply and demand of energy and they are required to make seasonal projections, e.g., to guarantee the security of energy supply during the coming winter, which becomes more di cult with the increased variability of energy production. The risk of not being able to satisfy the energy demand may be quanti ed in terms of the notion of Loss of load expectation (LOLE). Quoting from (NationalGrid, 2016), the LOLE is a \measure of the risk across the whole winter of demand exceeding supply under normal operation. It gives an indication of the amount of time across the whole winter that the System Operator may need to call on a range of emergency balancing tools to increase supply or reduce demand. » For instance, a cold winter characterised by weaker winds than normal may in some cases lead to a lack of energy if not enough other production means have been made available upstream to meet the energy demands.
*EDF scenario of 60% REN in the European energy mix (Burtin and Silva, 2015) by the European Network of Transmission System Operators for Electricity (ENTSOE), here for France and for the second week of January 2017 speci cally. It uses 14 cli-matic years to compute likely consumption and wind energy production. Informa-tion about the availability of other means of production for this winter, like nuclear plants in France, also plays a signi cant role in this sensitivity analysis. It shows that for low temperature and low wind energy capacity factor risks of de cit exist with the current European energy mix even after importing electricity from other countries (ENTSOE, 2016). It is thus essential to produce informative forecasts of surface wind speed at this timescale. Here, meteorological information comes only from a limited climatology (14 years). Note that we present here the risk of lower than expected production which is of high concern for TSOs, but the inverse risk of higher production than consumption is also hazardous as it may result in sharp drops of electricity prices.
In France, RTE (Reseau de Transport d’electricite) uses essentially the climato-logical surface wind speed to estimate the production at the seasonal scale. Indeed, at such long-term timescales, predictability of the weather is an open question, and it is particularly the case for surface variables which are in uenced by many small scale phenomena.
Nevertheless, some studies show good results in forecasting the monthly mean wind speed at several observation sites by using Arti cial Neural Network models (ANN) (Bilgili et al., 2007; More and Deo, 2003; Azad et al., 2014), giving an accu-rate trend of the wind speed a season ahead, but a limited information on the wind variability at higher frequency. Other authors forecasted daily mean wind speed at the seasonal scale using ANN (Azad et al., 2014; Wang et al., 2015; Guo et al., 2012).

Table of contents :

1 Résumé 
1.1 Introduction
1.2 Calibrated Ensemble Forecasts using Quantile Regression Forests and Ensemble Model Output Statistics
1.3 Forest-based Methods and Ensemble Model Output Statistics for Rainfall Ensemble Forecasting
1.4 CRPS-based Verification Tools for Extreme Events
1.5 Epilogue
2 Calibrated Ensemble Forecasts using Quantile Regression Forests and Ensemble Model Output Statistics
2.1 Introduction
2.2 Methods
2.3 Analysis of the French operational ensemble forecast system (PEARP)
2.4 Results
2.5 Discussion
2.6 Appendix
3 Forest-based Methods and Ensemble Model Output Statistics for Rainfall Ensemble Forecasting
3.1 Introduction
3.2 Quantile regression forests and gradient forests
3.3 Ensemble model output statistics and EGP
3.4 Case study on the PEARP ensemble prediction system
3.5 Results
3.6 Discussion
3.7 Appendix
4 CRPS-based Verification Tools for Extreme Events 
4.1 Introduction
4.2 Tail equivalence, wCRPS and choice of a weighting function
4.3 A CRPS-based tool using extreme value theory
4.4 Discussion
4.5 Appendix

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