FORECASTING & SYNTHETIC GENERATION OF HYDRO-CLIMATIC VARIABLES

PDF Version of this paper: https://www.doanalytics.net/Documents/DW-Hydroclimatic-Modeling-ENSO.pdf

INDEX

 1.    OPCHAIN-W&E&G: WATER & ELECTRICITY & GAS SUPPLY CHAIN OPTIMIZATION

1.1.   OPCHAIN-WATER: INTEGRATED WATER RESOURCES PLANNING SYSTEM

1.2.   OPCHAIN-E&G: ELECTRICITY & GAS SUPPLY CHAIN OPTIMIZATION

1.3.   OPCHAIN-SGO: SMART GRIDS OPTIMIZATION

 2.    SYNTHETIC GENERATION & FORECASTING OF HYDRO-CLIMATIC VARIABLES

2.1.   STATISTICAL SYNTHETIC GENERATION

2.2.   SYNTHETIC GENERATION USING MIX OF HISTORIC SERIES

3.    ENSO: EL NI?O SOUTHERN OSCILLATION

3.1.   FORECASTING ENSO EVENTS 

3.2.   FORECASTING HYDRO-CLIMATOLOGICAL VARIABLES USING ENSO FORECASTING

FORECASTING & SYNTHETIC GENERATION OF HYDRO-CLIMATIC VARIABLES

 1.    OPCHAIN-W&E&G: WATER & ELECTRICITY & GAS SUPPLY CHAIN OPTIMIZATION

 OPCHAIN-W&E&G is a Decision Support System of technical and economic planning tools that exploits the latest computer technologies coupled with the advanced mathematical modeling. The power of algorithms used for optimization, like Nested Benders Decomposition (NBD) or Generalized Stochastic Dual Dynamic Programming (G-SDDP), joint with the ability to represent precisely the relation of cost and volume, provides confidence in optimal results that cannot be provide by simpler approaches; its services for generation of models, coupled with spreadsheets, databases, multidimensional analysis tools, visualization software and Monte-Carlo simulation models to generate probabilistic scenarios; providing an ideal place to develop quickly and comprehensively optimization studies of the of water, electrical, smart grids and natural gas systems. OPCHAIN-W&E&G is composed by three models that can be integrated according to the needs of the end user.

1.1.   OPCHAIN-WATER: INTEGRATED WATER RESOURCES PLANNING SYSTEM

 For optimum management watershed, the hydraulic model may be use individually (OPCHAIN-WATER)

More information:

• Integrated Water Resources Planning System

https://www.dhirubhai.net/pulse/integrated-water-resources-planning-system-jesus-velasquez/

1.2.   OPCHAIN-E&G: ELECTRICITY & GAS SUPPLY CHAIN OPTIMIZATION

 OPCHAIN-ELE (ELEctricity Supply Chain Optimization) corresponds to a set of mathematical models designed to support the decisions of the various actors involved in the electricity supply chain, in terms of sectoral planning and business generation. According to the structure of modern electricity markets, the support of the business decision-making power generation should be seen from two different points of view.

Central agents: formed by the regulator, supervisor, planner and market operator

Generators: agents that operate power plants.

 OPCHAIN-GAS corresponds to a mathematical model designed to support the decisions of the various actors involved in the chain of supply of natural gas at the level of sectoral planning. OPCHAIN-ELE and OPCHAIN-GAS together make OPCHAIN-E&G a set of optimization model to dispatch the electricity and gas systems. OPCHAIN-E&G is designed to allow its users to parameterize the model according to the complexity of its supply chain and optimization requirements thereof.

More information:

• Electricity & Natural Gas - Advanced Supply Chain & Market Optimization

https://www.dhirubhai.net/pulse/electricity-natural-gas-advanced-supply-chain-jesus-velasquez/   

 1.3.   OPCHAIN-SGO: SMART GRIDS OPTIMIZATION

 OPCHAIN-SGO is a decision support system orient to Smart Grids Optimization. More information:

• Smart Grids Optimization & Renewables Energies

https://www.dhirubhai.net/pulse/smart-grids-optimization-jesus-velasquez/

 2.    SYNTHETIC GENERATION & FORECASTING OF HYDRO-CLIMATIC VARIABLES

 For the generation of synthetic scenarios of the variable climatic variables for stochastic optimization models, there are two requirements: i) short term (hours, days) and ii) medium/long term (weeks, months). Two types of predictions of the variables hydro climatic models related to water resources and management of renewable energies, such as wind, solar, maritime, are required

 Short-term or real-time models: based on methodologies such as the Kalman Filter, ARIMA,... . These models are not presented in this document. Interested readers are invited to read:

• Dynamic Machine Learning using a Multi-State Kalman Filter

https://www.dhirubhai.net/pulse/dynamic-machine-learning-using-multi-state-kalman-filter-velasquez/  

 Medium/long term models: based on methodologies of synthetic generation of random variables, discussed in this document.

For medium/long term, there are two alternatives to generate synthetic scenarios:

1.   Statistical synthetic generation model of climatic variables (type Fiering-Matalas),

2.   Generate synthetic series of climatic variables based on mixing of historical series

3.   Generate synthetic series based on the historical series having the ENSO (El Ni?o Southern Oscillation) series as an instrumental variable, this is the standard method in OPCHAIN-WATER.

2.1.   STATISTICAL SYNTHETIC GENERATION

 Statistical models for the synthetic generation of random variables are based on preserving in the synthetic series the first moments of the historical series (mean and variance-covariance matrices, lag 0 and lag 1), there are multiple models for this purpose, one of the models better known on the model of Matalas. This type of modeling is not discussed in this document. Interested readers are invited to read:

• Matalas N.C.. Mathematical Assessment of Synthetic Hydrology. Water Resources Research. Vol. 3, N°4, Pág. 937-945. (1967).

Based on assumptions of normality in the distributions of probability, it is worth noting that this type of models focuses on the modeling of the mean and the variance-covariance of processes, then they preserve these statistics in an appropriate way; but they do not guarantee the modeling properly the tails of probability distribution. This becomes a weakness when what is required in stochastic models is the management of financial and/or physical risk that are directly related to the tails of probability distributions.

The graph presents a visual comparison between the standard normal distribution function and the t-distribution, both have the same mean and similar variance, but their behavior in the queues is different. The normal distribution implies less risk, may be underestimated risk.

 Another aspect to consider is the asymmetry in the shape of the distribution. Most of the variable hydro-climatic are positive, which creates asymmetry in the tails of probability distribution function. Normally to address this problem are models based on a transformation of variables, an of the most used is the logarithm of the variable, it can be positive or negative and therefore it can be modelled with normal probability distributions. A distribution function whose domain are positive numbers, such as the chi-square, could also use.

 In any case, the synthetic generation model should be studied to be clear how it affects the behavior of the risks that is the goal of stochastic optimization models. OPCHAIN-WATER includes a synthetic generator based theory of Matalas.

 2.2.   SYNTHETIC GENERATION USING MIX OF HISTORIC SERIES

 Alternatively, to statistical models, it is common to use mixtures of periods of the historical series to set the pseudo-random scenarios. If it requires annual hydro-climatic scenarios, the procedure to follow is:

i)      If we have T years of complete historical data, which have been obtained by filling missing data of the original historical series using a statistically valid method.

ii)     It is possible to obtain up to T scenarios each of them beginning in the year t and including N (length in years of each scenario) consecutive years associate to tk that is defined as

tk=t+(N-1)      if t+(N-1) ≤ T , or equal to

tk=t+(N-1)-T   if t+(N-1) > T

 The previous process involves chaining historical series cyclically so that the year T is followed by the year 1.

The theoretical support of this methodology is:

i)      Historical series are a sample of a process that has occur un real-life, which is assumed is stationary (returns to the average maximum in T years) with internal seasonality, at monthly or weekly level (depends on the frequency of data of the historical series). Therefore, all the subseries are part of this stochastic process.

ii)     The historical series preserves the expected value, cross correlations, lag 0 and lag 1, of all the climatic hydro variable.

iii)    The historical series contains extreme events that have occur in the reality and, therefore, some of the subseries are linked to these events.

3.    ENSO EL NI?O SOUTHERN OSCILLATION

 ENSO (El Ni?o Southern Oscillation) events have proven to be determinants of climatological variables (water inflow, wind speed and solar luminosity) mainly in the Pacific Sea area; therefore; ENSO is a main variable to forecast events that may occur in the Pacific countries, but its effect impact all the world. ENSO impacts all the products derived from the use of water (hydro-electricity, water for irrigation/aqueducts/industries, …); the most important example is the spot price of electricity, that it is calculated as a proxy function of the marginal costs to meet the demand (dual variables of demand constraint).

 For this reason, it is valid and appropriate, take the ENSO as reference (instrumental variable) to model the hydro-climatic conditions that affect a water resources system to correlate these conditions with variables of the markets, mainly the electricity and water markets.

 EL NI?O event is the presence of abnormally warm waters (more than 0.5 °C above normal) on the South American Pacific coast of for more than three consecutive months. It is currently considered as an occasional, irregular and aperiodic phenomenon that impact the socio-economic variables in the world. It occurs with variable intensity, being 1982-1983 and 1997-1998 the most shocking episodes of during the 20th century.

On other occasions takes place the opposite phenomenon. The south trade winds (“vientos alisios del sur”) in Spanish) increase their intensity in the South American coast and they cause a greater upwelling of cold waters, which cover the surface of the Pacific Sea from South America to a little beyond of center of the Pacific Ocean. These event, with characteristics contrary to EL NI?O, is known as LA NI?A. 1988-1989, 1998-2000 and 2010-2011 episodes stand out for its intensity, duration and climate effect.

 The ENSO indicator most commonly used is the so-called NI?O 3.4 index (120-170W, 5S-5N). The graph presents the events in the period 1950-2013.

 3.1.   FORECASTING ENSO EVENTS 

 The importance of ENSO events has led to large amount of investigation by multiple organizations, which have multiple models oriented to forecast ENSO events in the short/medium term.

 The International Research Institute for Climate and Society (IRI, https://iri.columbia.edu/, Columbia University) public result of two projection methodologies of the ENSO index, which are described below:

i)      Subjective: Based on a consensus among analysts of the CPC (Climate Prediction Center) and IRI, in association with official CPC/IRI ENSO diagnostic discussion.

ii)     Objective: based on a Bayesian Ensemble Regression model that determines the weight factors to of each of the models available. Foer each model, the weight factor corresponds to the a-posteriori probability that the model is the correct model, based on the results obtained in the last period based on a combination of Bayesian models.

Two types of forecast models are used: i) Dynamic: based on the physical modeling of the dynamics of the process; and ii) Statistics: based on empirical evidence of the process adjusted through statistical models. The graph presents the predictions of the models included in the studies of the IRI

 The following chart summarizes the two predictions published by IRI on January 16, 2014.

For the reader's information, forecasts issued by IRI with the two type of models (physical and statistical) are presented for the period beginning on March 12, 2012 and extended for 22 months.

3.2.   FORECASTING HYDRO-CLIMATOLOGICAL VARIABLES USING ENSO FORECASTING

DW methodology is based on integrating the ENSO forecast of the IRI with the observed historical series of climatological variables. OPCHAIN-ENSO uses an optimization model of which results are the convex combination of historical series that “best” represent a synthetic scenario generated from the statistical characteristics of the IRI forecast. This process is valid for the first year of the scenarios, which is the period covered by the projections of the IRI.

 DW has developed a methodology for hydro-climatic variables prediction-based ENSO forecasting. The process is:

1.   The ENSO as a reference for the rest of the hydro-climatic variables

2.   IRI prediction of the is used to characterize the variability of ENSO in the short/medium term, as presents it the figure

3.   Synthetic series for the ENSO variable basis is generated using the variability of the prediction of the IRI. DW used a triangular distribution for this synthetic generation.

 4.   Generation of synthetic series of hydro-climatic variables by solving an optimization problem that minimizes the error of adjustment of IRI-synthetic ENSO series with a mix of historical ENSO series. This series have a length of one year. The objective of the model is to find for each IRI-synthetic ENSO serie a new DW-synthetic ENSO series built using a convex combination of historical ENSO series; this new synthetic serie must minimizes the difference in the two series: IRI-synthetic and DW-synthetic. Weights obtained in the optimization problem are used to generate hydro climatic synthetic series from the convex combination of historical series of the hydro climatic variables.

The synthetic series generated by this model can be used to study many optimization problems in bio-industrials supply chain and for planning renewables energies so like water, wing, solar radiation, temperature, … .

 If the lector is interested into know more about the structure of the optimization problem, can send an email to [email protected].