ArticlePDF Available

Simulation of water-energy fluxes through small-scale reservoir systems under limited data availability

Authors:

Abstract and Figures

We present a stochastic approach accounting for input uncertainties within water-energy simulations. The stochastic paradigm, which allows for quantifying the inherent uncertainty of hydrometeorological processes, becomes even more crucial in case of missing or inadequate information. Our scheme uses simplified conceptual models which are subject to significant uncertainties, to generate the inputs of the overall simulation problem. The methodology is tested in a hypothetical hybrid renewable energy system across the small Aegean island of Astypalaia, comprising a pumped-storage reservoir serving multiple water uses, where both inflows and demands are regarded as random variables as result of stochastic inputs and parameters.
Content may be subject to copyright.
ScienceDirect
Available online at www.sciencedirect.com
Available online at www.sciencedirect.com
ScienceDirect
Energy Procedia 00 (2017) 000–000
www.elsevier.com/locate/procedia
1876-6102 © 2017The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
The 15th International Symposium on District Heating and Cooling
Assessing the feasibility of using the heat demand-outdoor
temperature function for a long-term district heat demand forecast
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc
aIN+ Center for Innovation, Technology and Policy Research -Instituto Superior Técnico,Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal
bVeolia Recherche & Innovation,291 Avenue Dreyfous Daniel, 78520 Limay, France
cDépartement Systèmes Énergétiques et Environnement -IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
Abstract
District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the
greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat
sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease,
prolonging the investment return period.
The main scope of this paper is to assess the feasibility of using the heat demand outdoor temperature function for heat demand
forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665
buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district
renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were
compared with results from a dynamic heat demand model, previously developed and validated by the authors.
The results showed that when only weather change is considered, the margin of error could be acceptable for some applications
(the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation
scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered).
The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the
decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and
renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the
coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and
improve the accuracy of heat demand estimations.
© 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and
Cooling.
Keywords: Heat demand; Forecast; Climate change
Energy Procedia 125 (2017) 405–414
1876-6102 © 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientic committee of the European Geosciences Union (EGU) General Assembly 2017 – Division
Energy, Resources and the Environment (ERE).
10.1016/j.egypro.2017.08.078
10.1016/j.egypro.2017.08.078 1876-6102
© 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientic committee of the European Geosciences Union (EGU) General Assembly
2017 – Division Energy, Resources and the Environment (ERE).
Available online at www.sciencedirect.com
ScienceDirect
Energy Procedia00 (2017) 000–000
www.elsevier.com/locate/procedia
1876-6102© 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientific committee of the European Geosciences Union (EGU) General Assembly 2017
– Division Energy, Resources and the Environment (ERE).
European Geosciences Union General Assembly 2017, EGU
Division Energy, Resources & Environment, ERE
Simulation of water-energy fluxes through small-scale reservoir
systems under limited data availability
Konstantinos Papoulakosa,*, Giorgos Pollakisa, Yiannis Moustakisa, Apostolis
Markopoulosa, Theano Iliopouloua, Panayiotis Dimitriadisa, Demetris Koutsoyiannisa
and Andreas Efstratiadisa
a Department of Water Resources & Environmental Engineering, School of Civil Engineering, National Technical University of Athens, Heroon
Polytechniou 9, Zografou 15780, Greece
Abstract
We present a stochastic approach accounting for input uncertainties within water-energy simulations. The stochastic paradigm,
which allows for quantifying the inherent uncertainty of hydrometeorological processes, becomes even more crucial in case of
missing or inadequate information. Our scheme uses simplified conceptual models which are subject to significant uncertainties,
to generate the inputs of the overall simulation problem. The methodology is tested in a hypothetical hybrid renewable energy
system across the small Aegean island of Astypalaia, comprising a pumped-storage reservoir serving multiple water uses, where
both inflows and demands are regarded as random variables as result of stochastic inputs and parameters.
© 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientific committee of the European Geosciences Union (EGU) General Assembly 2017
– Division Energy, Resources and the Environment (ERE).
Keywords: stochastic simulation; hybrid renewable energy systems; reservoir management; parameter uncertainty; pumped-storage system
1. Introduction
Small islands are regarded as promising areas for developing hybrid water-energy systems that combine multiple
sources of renewable energy with pumped-storage facilities. The most essential element of such systems is the water
storage component (reservoir), which implements both flow and energy regulations. Apparently, the representation
* Corresponding author. Tel.: +30 210 77 22 831; fax: +30 210 77 22 831.
E-mail address: papoulakoskon@gmail.com
Available online at www.sciencedirect.com
ScienceDirect
Energy Procedia00 (2017) 000–000
www.elsevier.com/locate/procedia
1876-6102© 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientific committee of the European Geosciences Union (EGU) General Assembly 2017
– Division Energy, Resources and the Environment (ERE).
European Geosciences Union General Assembly 2017, EGU
Division Energy, Resources & Environment, ERE
Simulation of water-energy fluxes through small-scale reservoir
systems under limited data availability
Konstantinos Papoulakosa,*, Giorgos Pollakisa, Yiannis Moustakisa, Apostolis
Markopoulosa, Theano Iliopouloua, Panayiotis Dimitriadisa, Demetris Koutsoyiannisa
and Andreas Efstratiadisa
a Department of Water Resources & Environmental Engineering, School of Civil Engineering, National Technical University of Athens, Heroon
Polytechniou 9, Zografou 15780, Greece
Abstract
We present a stochastic approach accounting for input uncertainties within water-energy simulations. The stochastic paradigm,
which allows for quantifying the inherent uncertainty of hydrometeorological processes, becomes even more crucial in case of
missing or inadequate information. Our scheme uses simplified conceptual models which are subject to significant uncertainties,
to generate the inputs of the overall simulation problem. The methodology is tested in a hypothetical hybrid renewable energy
system across the small Aegean island of Astypalaia, comprising a pumped-storage reservoir serving multiple water uses, where
both inflows and demands are regarded as random variables as result of stochastic inputs and parameters.
© 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientific committee of the European Geosciences Union (EGU) General Assembly 2017
– Division Energy, Resources and the Environment (ERE).
Keywords: stochastic simulation; hybrid renewable energy systems; reservoir management; parameter uncertainty; pumped-storage system
1. Introduction
Small islands are regarded as promising areas for developing hybrid water-energy systems that combine multiple
sources of renewable energy with pumped-storage facilities. The most essential element of such systems is the water
storage component (reservoir), which implements both flow and energy regulations. Apparently, the representation
* Corresponding author. Tel.: +30 210 77 22 831; fax: +30 210 77 22 831.
E-mail address: papoulakoskon@gmail.com
406 Konstantinos Papoulakos et al. / Energy Procedia 125 (2017) 405–414
2 Konstantinos Papoulakos et al. / Energy Procedia 00 (2017) 000–000
of the overall water-energy management problem requires the simulation of the operation of the reservoir system,
which in turn requires a faithful estimation of water inflows and demands of water and energy. Yet, in small-scale
reservoir systems, this task is far from straightforward, since both the availability and accuracy of associated
information is generally very poor. In contrast to large-scale reservoir systems, for which it is quite easy to find
systematic and reliable hydrological data, in the case of small systems such data may be scarce or even missing,
which introduces further uncertainty to the inherently complex water-energy simulation problem.
The stochastic approach is the unique means to account for the multiple uncertainties within the combined water-
energy management problem. Using as pilot example the Livadi reservoir, which is a hypothetical pumped storage
component of the small Aegean island of Astypalaia (Greece), we provide a stochastic simulation framework, where
the time-varying reservoir inputs, i.e., inflows and demands, are subject to two different sources of uncertainty. The
first source is the long-term hydrometeorological uncertainty, which is typically tackled by using synthetic time
series that reproduce the statistical characteristics of the observed data, while the second source is associated with
the complex dynamics of the rainfall-runoff transformation, expressed by means of conceptual parameters. Yet, due
to the lack of historical runoff data, it is not possible to infer these parameters through the classical calibration
procedure, thus obtaining a unique rainfall-runoff transformation model [1]. For this reason, we take advantage of
the limited information about the hydrometeorological regime of the study area, to provide multiple “behavioural”
parameter sets, resulting to multiple stochastic responses of the water-energy system. The proposed modelling
scheme comprises stochastic and deterministic components, co-operating within a Monte Carlo simulation
framework.
2. Study area and data
Astypalaia (Αστυπάλαια) is a small Greek island (total area 97 km
2) with 1334 residents (2011 census), that
belongs to the Dodecanese complex (Fig. 1, left). The major water infrastructure of the island is the Livadi reservoir
(Fig. 1, right), having a useful storage capacity of 875 000 m3 (against a total capacity of 1 050 000 m3) and
extending over a maximum surface of 105 000 m2. The reservoir, which operates from 1998, fulfills domestic,
touristic and agricultural ware uses. The estimated annual demands are 210 000 m3 for water supply and 230 000 m3
for irrigation, most of which implemented during the summer period. The drainage basin upstream of the dam is 8
km2, producing ephemeral runoff. Unfortunately, across the Livadi basin there are no available any hydrometric
data, except for rough estimations about its hydrological regime. In particular, recent hydrological studies estimate
that about 15% of the mean annual rainfall is transformed to surface runoff, about 11% are underground losses that
are finally conducted to the sea, and the remaining quantity represents the evapotranspiration losses [2].
In the context of this pilot study, Livadi reservoir is assumed as the energy regulation component of a
hypothetical hybrid renewable energy system across the island, aiming at ensuring full autonomy against the
estimated electricity needs. In this respect, apart from the actual water uses, i.e., water supply and irrigation, we also
consider a small hydropower plant, installed at the discharge outlet (with maximum head of 32 m, i.e., equal to the
dam height) and a pump-storage tank, implementing daily regulations of energy surpluses and deficits, provided by
other renewable resources.
Fig. 1. Study area and location of Livadi reservoir (satellite images from Google Earth).
Konstantinos Papoulakos et al. / Energy Procedia 125 (2017) 405–414 407
Konstantinos Papoulakos et al. / EnergyProcedia 00 (2017) 000–000 3
3. Stochastic simulation procedure of water-energy fluxes
3.1. Overview
The outline of the modelling procedure is illustrated in Fig. 2.The simulation scheme, implemented at the daily time
scale, comprises of: (a) a stochastic model for generating synthetic rainfall and temperature time series; (b) a
radiation-based model, which transforms temperature to evaporation and potential evapotranspiration (PET); (c) a
stochastic rainfall-runoff model, whose parameters are represented as correlated random variables; (d) a stochastic
model for estimating water supply and irrigation demands, based on simulated temperature, PET and soil moisture;
and (e) a water management model of the reservoir system, providing stochastic forecasts of water and energy
outflows. Herein are given brief descriptions of each individual modelling component.
Fig. 2. Outline of the stochastic simulation procedure.
3.2. Stochastic simulation of meteorological drivers
The meteorological drivers of the simulation scheme are the daily rainfall and mean daily temperature. In
particular, rainfall is input of the hydrological model and the reservoir management model, while temperature is
input of the evaporation/PET model and the water demand model. Apparently, due to the intrinsically uncertain
nature of meteorological phenomena and the limited lengths of the historical data, it is essential to employ stochastic
approaches to represent the above non-deterministic inputs. On the one hand, this allows accounting for uncertainty
and large variability of the associated processes, and on the other hand, the use of synthetic time series, instead of
historical records, allows providing sufficiently large samples, in order to evaluate the system responses in statistical
terms (e.g., by means of reliability), with satisfactory accuracy [3].
408 Konstantinos Papoulakos et al. / Energy Procedia 125 (2017) 405–414
4 Konstantinos Papoulakos et al. / Energy Procedia 00 (2017) 000–000
For the generation of statistically consistent synthetic rainfall and temperature data we employed the stochastic
framework implemented within Castalia software [3]. This model uses state-of-the-art stochastic methodologies that
ensure the preservation of the essential statistical characteristics (marginal and joint distributions) of the parent
historical data at three time scales (annual, monthly, daily). Moreover, it reproduces the long-term persistence
(Hurst-Kolmogorov dynamics) at the annual and over-annual scales, the periodicity at the monthly scale, and the
rainfall intermittency (i.e., probability dry) at the daily scale.
3.3. Evaporation / potential evapotranspiration model
Theoretically, the evaporation from water surfaces, which is input of the reservoir management model, and the
potential evapotranspiration (PET) from vegetated surfaces (also called reference crop evapotranspiration), which is
input of the irrigation demand model, can be computed with high accuracy by the well-known Penman and Penman-
Monteith approaches, respectively, using as inputs four meteorological variables (air temperature, solar radiation,
relative humidity, wind velocity). However, in many cases, it is difficult to find simultaneous measurements of all
variables of interest, thus favoring the use of simplified approaches, using as single input the temperature.
In the proposed simulation scheme, we employ the radiation-based expression:
E = a Ra / (1 – c T) (1)
where E is the evaporation (or potential evapotranspiration) in mm, Ra (kJ m–2) is the extraterrestrial radiation, T (oC)
is the mean air temperature, and a (kg kJ–1) and c (oC–1) are model parameters that are inferred through calibration,
against “reference” data, which is estimated through the Penman (or Penman-Monteith) approaches [4]. We remark
that the extraterrestrial radiation is an astronomic variable, which is a periodic function of latitude and time, thus the
sole input of eq. (1) is the temperature, which can be easily obtained from a representative meteorological station.
3.4. Stochastic rainfall- runoff model
The key hydrological processes of the river basin upstream of Livadi dam, i.e., the transformation of rainfall to
actual evapotranspiration, surface runoff and underground losses to the sea, are modelled through a lumped
conceptual scheme, which uses three parameters. As illustrated in Fig. 2, the basin is vertically subdivided into two
storage elements that represent the temporary interception processes on the ground and the soil moisture accounting
across the saturated zone. Model inputs are the daily precipitation, P, and daily PET. All fluxes are expressed in
units of water depth (i.e., mm) per unit time (day), while storages are expressed in terms of water depths.
The model parameters are: (a) the interception capacity, Ia (mm), representing a rainfall threshold for runoff
generation, (b) the soil capacity K, (mm), and (c) the fraction, a of the soil storage that outflows to the sea, which
acts as a recession parameter. Initial condition of the model is the soil storage at the start of simulation, which may
be considered negligible (if the simulation starts at the end of the dry period) or expressed as fraction of K.
For given inputs and parameter values, the simulation procedure is the following. First, provided that P exceeds
the interception capacity, Ia, we employ the well-known SCS-CN formula for estimating the overland flow, i.e.:
Qoverland = (PIa)2 / (PIa + KS) (2)
where K S represents the so-called maximum potential soil retention (i.e., the empty space of the soil tank). The
latter is the key input parameter of the SCS-CN method, for which three typical values are generally considered,
depending on three antecedent soil moisture conditions. In the proposed model, this quantity is appropriately handled
as a continuous variable, depending on the current soil moisture storage, S [5].
The remaining rainfall is by priority used for fulfilling the PET demand, thus generating direct ET, i.e.
ETdirect = min (PET, PQoverland) (3)
while the remainder enters the soil moisture tank, thus increasing its current storage, i.e.:
Konstantinos Papoulakos et al. / Energy Procedia 125 (2017) 405–414 409
Konstantinos Papoulakos et al. / EnergyProcedia 00 (2017) 000–000 5
S=S0 + PQoverland – ETdirect (4)
where S0 denotes the soil moisture storage at the beginning of the time interval.
The actual evapotranspiration losses through the soil are estimated via the conceptual formula:
ETsoil = (PET – ETdirect)tanh(S/K) (5)
Next, a fraction a of the current storage moves vertically, thus generating underground losses to the sea, i.e.:
L = a (S– ETsoil) (6)
Finally, we check whether there is enough empty space in the tank, otherwise saturation excess runoff is produced
by means of spill, i.e.:
Qexcess = max(0, S– ETsoilLK) (7)
The total runoff is the sum of the overland and excess flow, while the total actual ET is the sum of the direct and
soil ET. At the end of the time step, we recalculate the current soil moisture storage, i.e.:
S0 = S– ETsoilLQexcess (8)
In case of missing observed runoff, the model is subject to major uncertainty, since it is not possible to identify its
parameters through calibration. This uncertainty is expressed in terms of a priori distributions of parameters; for
simplicity, Ia, K and a can be considered uniformly distributed within “reasonable” feasible ranges, specified via
hydrological evidence. In this respect, the model is stochastic, since its parameters are random variables.
3.5. Stochastic water demand model
For the estimation of drinking and agricultural water demands on a daily basis, we have developed two modules.
The first component, symbolized Dsupply, comprises a deterministic term, which accounts for seasonally-varying per
capita water needs and population projections (different for domestic and touristic use), and a stochastic term, which
is a function of the daily temperature.
On the other hand, the agricultural water module estimates the irrigation demand for four major crop categories
(arable, vegetable, orchard, and vineyard). The theoretical needs for each type are estimated on the basis of PET,
obtained from eq. (1), and the corresponding crop coefficient (different per month), obtained from [2]. Next, the
actual demand is estimated by considering the evapotranspiration deficit, i.e., the difference between PET and the
simulated actual evapotranspiration, ET, and an efficiency factor, e, depending on the irrigation method, i.e.:
Dirrigation = (PET– ET) / e (9)
We remark that the water supply component is only associated with the uncertainty of temperature, while the
uncertainty induced in the estimated demand for irrigation is subject to more sources of uncertainty, namely the
input uncertainty of rainfall and temperature, as well as the parameter uncertainty of the rainfall-runoff model.
3.6. Reservoir management model
For the representation of the daily operation of Livadi reservoir we consider the two aforementioned water uses,
putting water supply in first priority and irrigation in second, and we also consider a hypothetical power plant,
installed downstream of the intake; in case of abstractions for the fulfillment of drinking water or agricultural
demands, the water passes through the turbines, thus also producing hydroelectric energy. Moreover, in case of
storage surplus, and in order to avoid water losses due to spill, additional flow is conveyed through the turbines and
410 Konstantinos Papoulakos et al. / Energy Procedia 125 (2017) 405–414
6 Konstantinos Papoulakos et al. / Energy Procedia 00 (2017) 000–000
next conducted to the Livadi stream. The management policy is subject to storage and discharge capacity
constraints, as well as an external constraint, namely the preservation of a backup storage for employing energy
regulations within the in-daily pumping-storage cycle. We recall that in the context of the hypothetical renewable
energy system, the excess of energy produced by other renewable recourses (i.e., wind and solar parks) across the
island is consumed by pumping water to an upstream tank, and retrieved later as hydropower. This hypothetical tank
employs daily regulations, thus its capacity equals the backup storage of the downstream reservoir.
All inputs of the water management model are stochastic, i.e.:
Catchment runoff, provided by the stochastic hydrological model, driven by synthetic rainfall and temperature
and having uncertain parameters;
Rainfall over the lake area, synthetically generated;
Evaporation losses, estimated on the basis of synthetic temperature;
Water demand for domestic and touristic use, also depending on synthetic temperature;
Water demand for irrigation, estimated on the basis stochastic evapotranspiration deficits.
An explicit scheme is used to solve the reservoir simulation problem at the daily scale, assuming that at the
beginning of each time step the current storage and head are known, the latter being function of the former. Initially,
we add the net inflows (i.e., catchment runoff plus rainfall over the lake area minus evaporation losses) to the
current storage, and next we implement the outflows through the reservoir. By priority, we aim fulfilling the water
supply target, assuming that all active storage capacity is available for abstractions. Next, we fulfil irrigation
demands, yet now considering the storage above the backup volume, which is the sole control variable of the
problem. At the end, we check whether the current storage exceeds the reservoir capacity. In that case, we release
additional water, until exhausting the discharge capacity of the intake pipe. Whenever we release water, either for
satisfying the above uses or as surplus flow, for the sake of preventing water losses through the spillway, we
produce hydroelectric energy.
All model outputs (simulated storage, water release, spill losses and energy production) are stochastic, since they
depend both on stochastic inputs and the uncertain parameters of the rainfall-runoff procedure, which interrelate in a
complex manner. The system performance is evaluated in terms of reliability (i.e., probability of fulfilment of the
two water demands) and mean daily energy production. The reliability is estimated empirically as the percentage of
time that the actual outflow equals the corresponding demand. Apparently, the reliability of meeting the agricultural
demand depends on the value of the backup volume; the larger this value is, the lower the reliability.
4. Results and discussion
4.1. Generation of synthetic time series
Due to absence of reliable meteorological data in the island region, we obtained historical rainfall and
temperature records from the neighbouring island of Kalymnos, covering the period from June 2009 to February
2017. Based on these data, we generated daily synthetic time series for a 100 year simulation period, through the
Castalia stochastic weather generator model. The synthetic data preserve with high accuracy the statistical
properties, at the annual, monthly and daily temporal scales. Indicatively, in Table 1 we contrast the monthly
average and standard deviation values of the observed against simulated rainfall. Moreover, the increased length of
synthetic data, exhibiting the so-called Hurst-Kolmogorov behaviour, allows for providing rich patterns of potential
future realizations of the underlying processes and reproducing the changing behaviour of climate [6], which is
impossible to detect in the limited historical information (Fig. 3).
Table 1. Comparison of monthly statistical characteristics (average, standard deviation) of synthetic vs. observed rainfall.
Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep
Average, synthetic 42.0 88.3 160.6 153.4 98.7 58.8 40.8 16.2 4.5 7.1 0.6 11.1
Average, observed 37.4 77.4 143.7 143.5 98.5 56.0 34.8 14.3 3.8 0.0 0.5 10.0
St. dev., synthetic 27.4 89.9 102.7 44.0 47.9 31.1 38.3 10.3 6.5 0.7 1.1 13.2
St. dev., observed 26.9 80.8 110.0 48.6 43.4 33.0 33.6 9.7 6.7 0.0 1.3 13.5
Konstantinos Papoulakos et al. / Energy Procedia 125 (2017) 405–414 411
Konstantinos Papoulakos et al. / EnergyProcedia 00 (2017) 000–000 7
Fig. 3. Synthetic time series of annual rainfall (left) and temperature (right) and 10-year moving average for a 100-year horizon.
4.2. Rainfall-runoff model calibration under uncertainty
The rainfall-runoff model, detailed in Section 3.4, was used to provide stochastic estimations of the daily inflows
to the Livadi reservoir and the actual evapotranspiration through the study area, which was essential for estimating
the agricultural demands.
Model inputs were the 100-year daily synthetic rainfall, provided by Castalia model, and the daily synthetic PET,
provided by the parametric expression (1), using synthetic temperature, extraterrestrial radiation estimated for the
study area latitude (φ = 36 30΄)and parameters a and c interpolated from a neighbouring station.
To calibrate the model, in the absence of any observed runoff data, we receded to the use of available ‘soft’ data, i.e.,
rough estimates of the mean annual water balance of the basin, obtained from local expert knowledge. We recall that
a recent hydrological study estimated that the mean annual rainfall is partitioned into actual evapotranspiration,
surface runoff, and underground losses at ratios of 74, 15 and 11%, respectively.
For an a priori quantification of uncertainty, we employed 300 000 Monte Carlo simulations with synthetic
inputs (rainfall and PET), as resulting from 300 000 randomly generated parameter sets Ia, K and a. These were
assumed to be uniformly distributed in vast ‘feasible’ ranges, particularly [0, 70] for initial abstraction (mm), [10,
700] for soil capacity (mm), and [0, 0.01] for recession rate for percolation. For each simulation experiment, we
calculated the associated water balance estimates, i.e., the percentage of rainfall to actual evapotranspiration, surface
runoff, and underground losses, and distinguished the parameter sets satisfying the aforementioned ratios with a 5%
tolerance interval. This resulted to 2100 parameter sets, which are considered “behavioural”, in the sense that they
ensure a realistic representation of the macroscopic hydrological behaviour of this highly uncertain system [7].
Fig. 4. Scatter plots of all pairs of acceptable (behavioural) parameter sets.
412 Konstantinos Papoulakos et al. / Energy Procedia 125 (2017) 405–414
8 Konstantinos Papoulakos et al. / Energy Procedia 00 (2017) 000–000
Fig. 5. Histograms of behavioural parameters (2100 sets).
Fig. 6. Simulated runoff vs. synthetic rainfall assuming two extreme behavioural parameter sets (upper set: Ia = 57.8 mm, K = 194.7 mm, a =
0.00342; lower set: Ia = 0.8 mm, K = 424.2 mm, a = 0.00157).
This simple yet effective Monte Carlo procedure provided an a posteriori quantification of the model
uncertainty, together with insights into the nonlinear dependencies among the behavioural parameters (Fig. 4). In
general, the extent of the behavioural parameter space is quite large, and the dependency patterns are irregular. It
can be seen that in order to preserve the estimated water balance within the acceptable tolerance, the interception
capacity Ia, and the recession rate, a, should be both anti-correlated with the soil moisture capacity, K, which is
reasonable. In Fig. 5 we also plot the histograms of the three parameters, which exhibit different statistical
behaviour. We observe that K follows a heavy-tail distribution, Ia is uniformly distributed, while a is normally
distributed.
Although the water balance information helped restricting somehow the tremendous initial parameter
uncertainty, the remaining uncertainty is still very large. For instance, in Fig. 6 we contrast the simulated daily
runoff from two totally different parameter sets, corresponding to the extreme values of soil capacity.
For all behavioural parameter sets, we ran the rainfall-runoff model in stochastic mode, thus providing 2100
scenarios of potential basin responses. The main outcomes of the model, i.e., synthetic actual evapotranspiration and
runoff, were next used to feed to water demand and reservoir operation model, respectively.
4.3. Estimation of water demands
As explained in section 3.5, the simulated drinking water demand depends on temperature, which is provided by
the Castalia model, while the irrigation demand depends both on temperature and the simulated actual
Konstantinos Papoulakos et al. / Energy Procedia 125 (2017) 405–414 413
Konstantinos Papoulakos et al. / EnergyProcedia 00 (2017) 000–000 9
evapotranspiration, which is output of the rainfall-runoff model. In this respect, for the former we generate a unique
synthetic time series of 100 years length, while for the latter we generate 2100 scenarios, associated with the
behavioural outcomes of the hydrological model. On mean daily basis, the water supply demand is 578 m3, while the
agricultural demand ranges between 550 and 675 m3, reflecting the relatively small variability of actual ET. On the
other hand, the seasonal variability of both processes is significant, due to climatic and socioeconomic reasons
(substantial increase of summer population, due to tourism).
4.4. Simulation of Livadi reservoir
We ran the reservoir management model in Monte Carlo setting, considering 2100 runoff and irrigation demand
scenarios, as well as a common scenario for synthetic rainfall, evaporation and water supply data. From this
procedure, we obtained 2100 scenarios of the daily operation of the system for 100 simulated years, by setting a
backup storage constraint up to 50 000 m3. The key quantity of interest is the mean daily hydropower production,
which was used for creating the energy mix of the island [8]. This variable should be represented by a bounded
distribution, due to the existence of the head constraint. In Fig. 7, it is shown that the Beta distribution has a
satisfactory fit to the mean daily hydropower production.
Fig. 7. Fitting of the Beta distribution to standardized mean daily hydropower production values.
4.5. Analysis of parameter and process dependencies
This analysis aims at investigating how the parameter uncertainty of the rainfall-runoff model is propagated to
next simulations.Fig.8 shows scatter plots of the mean daily runoff, irrigation demand and hydropower production
against the full range of behavioural values of soil moisture capacity, K. As expected on physical grounds, an
increased soil moisture capacity is associated with less surface runoff and decreased irrigation demands. The mean
daily energy production potential is also decreased for larger values of the K parameter, yet in a less unambiguous
way as shown in Fig. 5(c). At this final modelling stage of hydropower simulation, the uncertainty that initiated from
the rainfall-runoff simulations is propagated through the sequence of models used and amplified due to the inter-
relation of the inputs in the different models. The increased complexity of the model at this stage -also enhanced by
the set of operational rules imposed- together with the variability induced from the meteorological forcing makes
tracing back the physical drivers more difficult than in the previous cases. For example, an increased soil moisture
capacity would lead to less runoff, but also less irrigation needs, since more soil moisture can be retained in the
unsaturated zone. In this respect, the unique approach to reveal and quantify such complex trade-offs is through
Monte Carlo analysis.
414 Konstantinos Papoulakos et al. / Energy Procedia 125 (2017) 405–414
10 Konstantinos Papoulakos et al. / Energy Procedia 00 (2017) 000–000
Fig. 8. (a) Mean daily runoff (output of hydrological model, input of reservoir model) vs. behavioural soil moisture capacity values; (b) Mean
daily demand for irrigation (depends on simulated evapotranspiration deficits) vs. behavioural soil moisture capacity values; (c) Mean daily
hydropower production vs. behavioural soil moisture capacity values
5. Conclusions
This study highlights the value of stochastic approaches to handle the different sources of uncertainty, both case-
specific, i.e., data limitations in data-scarce regions, and inherent, i.e., emerging from the complexity of modelled
systems (e.g., multi-purpose hybrid renewable energy systems). Actually, the improper representation of uncertainty
is an intrinsic drawback of all deterministic hydrological and water management models, which are prone to limited
information provided by historical data. Combinations of hard (observations) and soft (human evidence based on
experience) information can help reducing yet never eliminating uncertainties. Moreover, complex water-energy
management problems suffer from multiple sources of uncertainties, since many of their inputs are not directly
obtained from in situ measurements but are generated through models or sequences of models, where uncertainties
are propagated from model to model.
For this reason, stochastic approaches are unique means to quantifying uncertainties, yet they do require careful
interpretation of their outcomes, since they may result to very large uncertainty bounds that seem difficult to take
advantage in practice. On the other hand, the awareness of modelling limitations due to uncertainty is absolutely
crucial to avoid overconfidence into deterministic approaches and to concentrate our efforts towards systematic and
reliable data, which is the sole way to reduce uncertainty.
References
[1] Efstratiadis, Andreas, Ioannis Nalbantis, and Demetris Koutsoyiannis (2015) “Hydrological modelling of temporally-varying catchments:
Facets of change and the value of information.” Hydrological Sciences Journal 60.7-8 (2015): 1438–1461.
[2] Aegean Hydrosystems Joint-Venture (2005) “Astypalaia Island.” In: Development of Systems and Tools for Water Resources Management of
Dodecanese Water District – Phase A, Report 1, Ministry of Development.
[3] Efstratiadis, Andreas, Yiannis Dialynas, Stefanos Kozanis, and Demetris Koutsoyiannis (2014) “A multivariate stochastic model for the
generation of synthetic time series at multiple time scales reproducing long-term persistence” Environmental Modelling & Software 62
(2014): 139–152.
[4] Tegos, Aristotelis, Andreas Efstratiadis, and Demetris Koutsoyiannis (2013) “A parametric model for potential evapotranspiration estimation
based on a simplified formulation of the Penman-Monteith equation.” In: Stavros Alexandris (ed.) Evapotranspiration - An Overview, 143–
165, InTech.
[5] Efstratiadis, Andreas, Antonios D. Koussis, Demetris Koutsoyiannis, and Nikos Mamassis (2014) “Flood design recipes vs. reality: can
predictions for ungauged basins be trusted?Natural Hazards and Earth System Sciences 14 (2014): 1417–1428.
[6] Koutsoyiannis, Demetris (2011) “Hurst-Kolmogorov dynamics and uncertainty.” Journal of the American Water Resources Association 47.3
(2011): 481–495.
[7] Beven, Keith. J., Andrew M. Binley (1992) “The future of distributed models: model calibration and uncertainty prediction.” Hydrological
Processes 6.3 (1992): 279-298.
[8] Stamou, Paraskevi, Sofia Karali, Maria Chalakatevaki, Vassiliki Daniil, Katerina Tzouka, Panayiotis Dimitriadis, Theano Iliopoulou, Panos
Papanicolaou, Demetris Koutsoyiannis, and Nikos Mamassis (2017) “Creating the electric energy mix of a non-connected Aegean island.”
EGU General Assembly 2017, Geophysical Research Abstracts, Vol. 19, Vienna, EGU2017-10130-10, European Geosciences Union.
... Table 20.2 summarizes the outcomes from two case scenarios, based on a preliminary (but indicative) analysis where each source has to be harvested according to the energy demand (Mavroyeoryos et al. 2017) and economic analysis (Karakatsanis et al. 2017) for the selected case. Therefore, a separate stochastic and cost analysis was first employed for solar energy (Koudouris et al. 2017), wind and marine energy (Moschos et al. 2017), hydropower with a pumped storage system (Papoulakos et al. 2017), biomass and geothermal energy (Chalakatevaki et al. 2017). The second case that was finally selected includes two wind turbines of 75 m height, 3800 m 2 of photovoltaic panels, two wave converter installations, addition of a small hydro turbine to the existing dam, a biomass facility fed with 180 t/year of cultivated biomass, and a pumped storage system that includes a reservoir with storage capacity of 0.5 hm 3 , a 2 km penstock and a hydro turbine installation. ...
... For instance, the efficiency curves of hydro turbines are typically extracted from laboratory models, and they are next adjusted to fit the prototype, by employing empirical corrections; next they are prone to damages and aging of the equipment over time, thus their actual value is by definition uncertain (Paish 2002;Sakki et al. 2020). Nevertheless, a generalized stochastic simulation framework should describe both process and model uncertainties, as is done in a case study of a hypothetical system by Papoulakos et al. (2017). ...
Chapter
The fundamental concepts in the field of water-energy systems and their historical evolution with emphasis on recent developments are reviewed. Initially, a brief history of the relation of water and energy is presented and the concept of the water-energy nexus in the 21th century is introduced. The investigation of the relationship between water and energy shows that this relationship comprises both conflicting and synergistic elements. Hydropower is identified as the major industry of the sector and its role in addressing modern energy challenges by means of integrated water-energy management is highlighted. Thus, the modelling steps of designing and operating a hydropower system are reviewed, followed by an analysis of theory and physics behind energy hydraulics. The key concept of uncertainty, which characterises all types of renewable energy, is also presented in the context of the design and management of water-energy systems. Subsequently, environmental considerations and impacts of using water for energy generation are discussed, followed by a summary of the developments in the emerging field of maritime energy. Finally, present challenges and possible future directions are presented.
... The possibility of hydropower production in the island was also studied and a simulation framework for small-scale reservoir systems was modelled Papoulakos et al., 2017), in association with high solar (Koudouris et al., 2017), wind and wave energy (Moschos et al., 2017). The potential of deploying agricultural residues, as well as cultivating energy crops with low irrigation demands for biomass energy production, was investigated. ...
... Recent analyses concerning the renewable energy design and management for the non-connected island of Astypalaia have illustrated how the uncertainty of several renewable energy sources can be efficiently managed through stochastic analysis (Chalakatevaki et al., 2017;Papoulakos et al., 2017). Therefore, stochastic analysis is essential in the renewable energy management both for the analysis of predictability of the related natural processes and for the analysis of the system dynamics and optimal design and operation under increased uncertainty. ...
Article
Full-text available
The ever-increasing energy demand has led to overexploitation of fossil fuels deposits, while renewables offer a viable alternative. Since renewable energy resources derive from phenomena related to either atmospheric or geophysical processes, unpredictability is inherent to renewable energy systems. An innovative and simple stochastic tool, the climacogram, was chosen to explore the degree of unpredictability. By applying the climacogram across the related timeseries and spatial-series it was feasible to identify the degree of unpredictability in each process through the Hurst parameter, an index that quantifies the level of uncertainty. All examined processes display a Hurst parameter larger than 0.5, indicating increased uncertainty on the long term. This implies that only through stochastic analysis may renewable energy resources be reliably manageable and cost efficient. In this context, a pilot application of a hybrid renewable energy system in the Greek island of Astypalaia is discussed, for which we show how the uncertainty (in terms of variability) of the input hydrometeorological processes alters the uncertainty of the output energy values.
... This work was conducted in the framework of the European Geosciences Union's 2017 General Assembly, where the students of School of Civil Engineering participated. The model was tested among the analysis conducted for this thesis and the complete work regarding the Astypalaia Island can be found under Papoulakos et al. (2017). The name of the model was inspired by the name of one of the developers, namely, Theano (Annie) Iliopoulou. ...
... More specifically, we have set the parameters as follows; (Beven, 1993). Further investigation and a more complete Monte-Carlo scheme under which multiple sets of parameters were determined can be found under Papoulakos et al. (2017). ...
Thesis
Full-text available
Typically, flood modelling in the context of everyday engineering practices is addressed through event-based deterministic tools, e.g., the well-known SCS-CN method. A major shortcoming of such approaches is the ignorance of uncertainty, which is associated with the variability of soil moisture conditions and the variability of rainfall during the storm event. In event-based modelling, the sole expression of uncertainty is the return period of the design storm, which is assumed to represent the acceptable risk of all output quantities (flood volume, peak discharge, etc.). In the meantime, the varying antecedent soil moisture conditions across the basin are represented by means of scenarios (e.g., the three AMC types by SCS), while the temporal distribution of rainfall is represented through standard deterministic patterns (e.g., the alternating blocks method). Furthermore, time of concentration is considered as a constant characteristic feature of a basin, which has actually been proved to be an invalid assumption. In order to address these major inconsistencies, while simultaneously preserving the simplicity and parsimony of the SCS-CN method, we have developed a quasi-continuous stochastic simulation approach, suitable for ungauged basins, comprising the following steps: (1) generation of synthetic daily rainfall time series; (2) update of potential maximum soil retention, on the basis of accumulated five-day Antecedent Precipitation; (3) estimation of daily runoff through the SCS-CN formula, using as inputs the daily rainfall and the updated value of maximum soil retention;(4) daily update of the value of time of concentration according to the runoff generated; (5) selection of extreme events and application of the standard SCS-CN procedure for each specific event. This scheme requires the use of two stochastic modelling components, namely the CastaliaR model, for the generation of synthetic daily data, and the HyetosMinute model, for the stochastic disaggregation of daily rainfall to finer temporal scales. Outcomes of this approach are a large number of synthetic flood events, allowing for expressing the design variables in statistical terms and thus properly evaluating flood risk. The proposed quasi-continuous stochastic simulation framework, along with a series of model variations is thoroughly investigated, in order to examine its response, prove its consistency and suggest further improvements and topics for future work.
... Regarding the hydroclimatic conditions presented in [5], 100 years of rainfall data and mean monthly temperature are generated. The time series produced are based on historic hydrometeorological data from June 2009 to February 2017. ...
... An upgrade of the existing dam into a hydroelectric dam is the basis of the proposed solution. A turbine of 0.08 MW is proposed in order to produce 25 MWh per year [5]. ...
Article
Full-text available
As the electric energy in the non-connected islands is mainly produced by oil-fueled power plants, the unit cost is extremely high due to import cost. The integration of renewable resources in the energy mix is essential for reducing the financial and environmental cost. In this work, various energy resources (renewable and fossil fuels) are evaluated using technical, environmental and economic criteria with an emphasis to biomass, pumped hydro storage and replacement of oil power plants. Finally, a synthesis is presented as a toy-model in an Aegean island that satisfies the electric energy demand including base and peak electric loads.
... Hydrological modelling can be assessed stochastically by generating synthetic data for a long simulation period and estimating performance with statistics (Efstratiadis et al. 2015). Papoulakos et al. (2017) deployed a stochastic simulation of a hydrological model at the Livadi reservoir in Astypalaia (Greece) as a hypothetical pilot example, where all inputs, such as surface runoff, rainfall, and evaporation were stochastic, and Monte Carlo analysis was used. Different scenarios of the reservoir's daily operation are calculated using the reservoir management model. ...
Article
Sustainable mine closure is one of the main priorities of the mining industry. The aim of this research was to predict the spatiotemporal development of water levels in a mined-out pit by generating forecasts of the dependent variables (rainfall and temperature) via linear (autoregressive integrated moving average) and non-linear (artificial neural network) models. We investigated natural water level development in one mined-out pit of the closed lignite mines in Amynteon, north Greece, with no artificial recharge. The forecasted rate of water level increase was estimated to be ≈ 10 m per year in the ‘early’ stage of pit lake spatiotemporal evolution (first 10 years), and 0.1 m per year in the ‘last’ stage of potential lake development (after year 2060). Also, the optimum lake surface (i.e. the level where no significant increase in water level rate appears) was estimated at + 520 m, which was predicted to occur in ≈ 40 years. The proposed methodology was validated via water level measurements performed during the first year of lake development, where field measurements of water elevations closely followed predictions. Forecasting pit lake water levels is essential for strategic planning, examining pit lake repurposing options, and informing decisions about post-mining futures and economic transitions.
... For a review of such studies, see [7,13] and references therein, where also a massive globalscale analysis in the scale domain is included for several hydrological-cycle processes (i.e., near-surface air temperature, dew point, humidity, atmospheric pressure, near-surface wind speed, streamflow and precipitation) and microscale turbulent processes (such as grid turbulence and turbulent jets). Alternative scientific fields, where the analysis is performed in the scale domain and by using the climacogram, include studies of rock formations [32], landscapes [37,38], water-energy nexus [60,61], time-irreversible processes [62,63], multilayer perceptron [64] and many others [65] as shown in the applications of the entry. It is again emphasized that this entry focuses on the multi-dimensional spatio-temporal stochastic metrics in the scale domain, as presented in the next sections. ...
Article
Full-text available
The stochastic analysis in the scale domain (instead of the traditional lag or frequency domains) is introduced as a robust means to identify, model and simulate the Hurst–Kolmogorov (HK) dynamics, ranging from small (fractal) to large scales exhibiting the clustering behavior (else known as the Hurst phenomenon or long-range dependence). The HK clustering is an attribute of a multidimensional (1D, 2D, etc.) spatio-temporal stationary stochastic process with an arbitrary marginal distribution function, and a fractal behavior on small spatio-temporal scales of the dependence structure and a power-type on large scales, yielding a high probability of low- or high-magnitude events to group together in space and time. This behavior is preferably analyzed through the second-order statistics, and in the scale domain, by the stochastic metric of the climacogram, i.e., the variance of the averaged spatio-temporal process vs. spatio-temporal scale.
... In the field of hydrology, the study of time series and their synthetic generation is of great importance. They are used to drive models in a wide range of applications, from reservoir design [1][2][3] and planning [4][5][6][7], ecological flow estimation [8], to flood risk [9]. There are a fair amount of models available in the literature and despite potential differences between them, they share two common goals: i) adequate modeling of the marginal distribution and ii) adequate characterization of the auto-correlation structure. ...
Article
Full-text available
The generation of synthetic time series is important in contemporary water sciences for their wide applicability and ability to model environmental uncertainty. Hydroclimatic variables often exhibit highly skewed distributions, intermittency (that is, alternating dry and wet intervals), and spatial and temporal dependencies that pose a particular challenge to their study. Vine copula models offer an appealing approach to generate synthetic time series because of their ability to preserve any marginal distribution while modeling a variety of probabilistic dependence structures. In this work, we focus on the stochastic modeling of hydroclimatic processes using vine copula models. We provide an approach to model intermittency by coupling Markov chains with vine copula models. Our approach preserves first-order auto- and cross-dependencies (correlation). Moreover, we present a novel framework that is able to model multiple processes simultaneously. This method is based on the coupling of temporal and spatial dependence models through repetitive sampling. The result is a parsimonious and flexible method that can adequately account for temporal and spatial dependencies. Our method is illustrated within the context of a recent reliability assessment of a historical hydraulic structure in central Mexico. Our results show that by ignoring important characteristics of probabilistic dependence that are well captured by our approach, the reliability of the structure could be severely underestimated.
... • Identification and separation of single-purpose hydroelectric reservoirs and multipurpose hydroelectric reservoirs: It is common for hydroelectric projects to be combined with other water 515 uses as part of multi-purpose reservoirs [98,113]. In particular, according to data from the International Commission on Large Dams, out of the 5786 hydroelectric dams globally 3932 are multi-purpose dams [114]. ...
Article
Full-text available
Landscape impacts associated with aesthetics have been a persistent cause of opposition against renewable energy projects. However, the current uncertainty over the spatial extents and the rationality of reported impacts impedes the development of optimal strategies for their mitigation. In this paper, a typology of landscape impacts is formed for hydroelectric, wind and solar energy through the review of three metrics that have been used extensively for impact-assessment: land use, visibility and public perception. Additionally, a generic landscape-impact ranking is formed, based on data from realized projects, demonstrating that hydroelectric energy has been the least impactful to landscapes per unit energy generation, followed by solar and wind energy, respectively. More importantly, the analysis highlights the strengths and weaknesses of each technology, in a landscape impact context, and demonstrates that, depending on landscape attributes, any technology can potentially be the least impactful. Finally, a holistic approach is proposed for future research and policy for the integration of renewable energy to landscapes, introducing the maximum utilization of the advantages of each technology as an additional strategy in an effort to expand beyond the mitigation of negative impacts.
... However, natural processes with HK behaviour abound in literature. For example, turbulent processes exhibit such long-term persistent behaviour (e.g., Dimitriadis et al., 2016a, and references therein), recently in ecosystem variability (Pappas et al., 2017) as well as most geophysical processes as verified in several cases (Koutsoyiannis, 2003;O'Connell et al., 2016;, and specifically in key hydrometeorological processes such as: river discharge and stage (Hurst, 1951;Koutsoyiannis et al., 2008;Markonis et al., 2017); solar radiation and wind speed Tsekouras and Koutsoyiannis, 2014;Koudouris et al., 2017); precipitation Dimitriadis et al., 2016a;; paleoclimatic temperature reconstructions ; temperature and dew point Lerias et al., 2016) and thus, humidity; potential evapotranspiration which can be adequately evaluated only by temperature and deterministic extraterrestrial radiation (Tegos et al., 2017) and therefore, a similar Hurst parameter as in temperature is expected; but also other renewable-energy related processes, such as wave energy and period , as well as processes used in energy production and management (Chalakatevaki et al., 2017;Papoulakos et al, 2017;Mayrogeorgios et al., 2017), but also weather finance models (Karakatsanis et al., 2017). Interestingly, in most of the aforementioned processes (if treated properly within a robust physical and statistical framework, e.g. by adjusting the process for sampling errors as well as discretization and bias effects) the Hurst parameter is estimated at the range 0.8 to 0.85, as indicated by Hurst ...
Thesis
Full-text available
The high complexity and uncertainty of atmospheric dynamics has been long identified through the observation and analysis of hydroclimatic processes such as temperature, dew-point, humidity, atmospheric wind, precipitation, atmospheric pressure, river discharge and stage etc. Particularly, all these processes seem to exhibit high unpredictability due to the clustering of events, a behaviour first identified in Nature by H.E. Hurst in 1951 while working at the River Nile, although its mathematical description is attributed to A. N. Kolmogorov who developed it while studying turbulence in 1940. To give credits to both scientists this behaviour and dynamics is called Hurst-Kolmogorov (HK). In order to properly study the clustering of events as well as the stochastic behaviour of hydroclimatic processes in general we would require numerous of measurements in annual scale. Unfortunately, large lengths of high quality annual data are hardly available in observations of hydroclimatic processes. However, the microscopic processes driving and generating the hydroclimatic ones are governed by turbulent state. By studying turbulent phenomena in situ we may be able to understand certain aspects of the related macroscopic processes in field. Certain strong advantages of studying microscopic turbulent processes in situ is the recording of very long time series, the high resolution of records and the controlled environment of the laboratory. The analysis of these time series offers the opportunity of better comprehending, control and comparison of the two scientific methods through the deterministic and stochastic approach. In this thesis, we explore and further advance the second-order stochastic framework for the empirical as well as theoretical estimation of the marginal characteristic and dependence structure of a process (from small to extreme behaviour in time and state). Also, we develop and apply explicit and implicit algorithms for stochastic synthesis of mathematical processes as well as stochastic prediction of physical processes. Moreover, we analyze several turbulent processes and we estimate the Hurst parameter (H >> 0.5 for all cases) and the drop of variance with scale based on experiments in turbulent jets held at the laboratory. Additionally, we propose a stochastic model for the behaviour of a process from the micro to the macro scale that results from the maximization of entropy for both the marginal distribution and the dependence structure. Finally, we apply this model to microscale turbulent processes, as well as hydroclimatic ones extracted from thousands of stations around the globe including countless of data. The most important innovation of this thesis is that, to the Author’s knowledge, a unique framework (through modelling of common expression of both the marginal density distribution function and the second-order dependence structure) is presented that can include the simulation of the discretization effect, the statistical bias, certain aspects of the turbulent intermittent (or else fractal) behaviour (at the microscale of the dependence structure) and the long-term behaviour (at the macroscale of the dependence structure), the extreme events (at the left and right tail of the marginal distribution), as well as applications to 13 turbulent and hydroclimatic processes including experimentation and global analyses of surface stations (overall, several billions of observations). A summary of the major innovations of the thesis are: (a) the further development, and extensive application to numerous processes, of the classical second-order stochastic framework including innovative approaches to account for intermittency, discretization effects and statistical bias; (b) the further development of stochastic generation schemes such as the Sum of Autoregressive (SAR) models, e.g. AR(1) or ARMA(1,1), the Symmetric-Moving-Average (SMA) scheme in many dimensions (that can generate any process second-order dependence structure, approximate any marginal distribution to the desired level of accuracy and simulate certain aspects of the intermittent behaviour) and an explicit and implicit (pseudo) cyclo-stationary (pCSAR and pCSMA) schemes for simulating the deterministic periodicities of a process such as seasonal and diurnal; and (c) the introduction and application of an extended stochastic model (with an innovative identical expression of a four-parameter marginal distribution density function and correlation structure, i.e. g(x;C)=λ/[(1+|x/a+b|^c )]^d, with C=[λ,a,b,c,d]), that encloses a large variety of distributions (ranging from Gaussian to powered-exponential and Pareto) as well as dependence structures (such as white noise, Markov and HK), and is in agreement (in this form or through more simplified versions) with an interestingly large variety of turbulent (such as horizontal and vertical thermal jet of positively buoyancy processes using laser-induced-fluorescence techniques as well as grid-turbulence generated within a wind-tunnel), geostatistical (such as 2d rock formations), and hydroclimatic processes (such as temperature, atmospheric wind, dew-point and thus, humidity, precipitation, atmospheric pressure, river discharges and solar radiation, in a global scale, as well as a very long time series of river stage, and wave height and period). Amazingly, all examined physical processes (overall 13) exhibited long-range dependence and in particular, most (if treated properly within a robust physical and statistical framework, e.g. by adjusting the process for sampling errors as well as discretization and bias effects) with a mean long-term persistence parameter equal to H ≈ 5/6 (as in the case of isotropic grid-turbulence), and (for the processes examined in the microscale such atmospheric wind, surface temperature and dew-point, in a global scale, and a long duration discharge time series and storm event in terms of precipitation and wind) a powered-exponential behaviour with a fractal parameter close to M ≈ 1/3 (as in the case of isotropic grid-turbulence).
... Simulation of water-energy fluxes through small-scale reservoir systemsSimulation framework comprising: (a) synthetic rainfall and temperature; (b) rainfall-runoff model; (c) water supply and irrigation demands, and (d) daily operation model of the reservoir system. For more information see in[3]. ...
Presentation
Full-text available
Non-connected islands to the electric gird are often depending on oil-fueled power plants with high unit cost. A hybrid energy system with renewable resources such as wind and solar plants could reduce this cost and also offer more environmental friendly solutions. However, atmospheric processes are characterized by high uncertainty that does not permit harvesting and utilizing full of their potential. Therefore, a more sophisticated framework that somehow incorporates this uncertainty could improve the performance of the system. In this context, we describe several stochastic and financial aspects of this framework. Particularly, we investigate the cross-correlation between several atmospheric processes and the energy demand, the possibility of mixing renewable resources with the conventional ones and in what degree of reliability, and critical financial subsystems such as weather derivatives. A pilot application of the above framework is also presented for a remote island in the Aegean Sea.
Article
Full-text available
As the electric energy in the non-connected islands is mainly produced by oil-fueled power plants, the unit cost is extremely high due to import cost. The integration of renewable resources in the energy mix is essential for reducing the financial and environmental cost. In this work, various energy resources (renewable and fossil fuels) are evaluated using technical, environmental and economic criteria with an emphasis to biomass, pumped hydro storage and replacement of oil power plants. Finally, a synthesis is presented as a toy-model in an Aegean island that satisfies the electric energy demand including base and peak electric loads.
Article
Full-text available
Despite the great scientific and technological advances in flood hydrology, everyday engineering practices still follow simplistic approaches that are easy to formally implement in ungauged areas. In general, these "recipes" have been developed many decades ago, based on field data from typically few experimental catchments. However, many of them have been neither updated nor validated across all hydroclimatic and geomorphological conditions. This has an obvious impact on the quality and reliability of hydrological studies, and, consequently, on the safety and cost of the related flood protection works. Preliminary results, based on historical flood data from Cyprus and Greece, indicate that a substantial revision of many aspects of flood engineering procedures is required, including the regionalization formulas as well as the modelling concepts themselves. In order to provide a consistent design framework and to ensure realistic predictions of the flood risk (a key issue of the 2007/60/EU Directive) in ungauged basins, it is necessary to rethink the current engineering practices. In this vein, the collection of reliable hydrological data would be essential for re-evaluating the existing "recipes", taking into account local peculiarities, and for updating the modelling methodologies as needed.
Chapter
Full-text available
Evaporation can be viewed both as energy (heat) exchange and an aerodynamic process. According to the energy balance approach, the net radiation at the Earth’s surface (Rn = Sn – Ln, where Sn and Ln are the shortwave—solar—and longwave—earth—radiation, respectively) is mainly transformed to latent heat flux, Λ, and sensible heat flux to the air, H. The evaporation rate, expressed in terms of mass per unit area and time (e.g. kg/m²/d), is given by the ratio E΄ := Λ / λ, where λ is the latent heat of vaporization, with typical value 2460 kJ/kg. By ignoring fluxes of lower importance, such as soil heat flux, the heat balance equation is solved for evaporation, yielding: where b := H / Λ is the co-called Bowen ratio. The estimation of b requires the measurement of temperature at two levels (surface and atmosphere), as well as the measurement of humidity at the atmosphere. On the other hand, the estimation of the net radiation Rn is based on a radiation balance approach to determine the components Sn and Ln. Typical input data required (in addition to latitude and time of the year), are solar radiation (direct and diffuse, or, in absence of them, sunshine duration data or cloud cover observations), temperature and relative humidity. The net radiation also depends of surface properties (i.e. albedo) and topographical characteristics, in terms of slope, aspect and shadowing. Recent studies proved that the impacts of topography are important at all spatial scales, although they are usually neglected in calculations [23]. where Δ is the slope of vapor pressure/temperature curve at equilibrium temperature (hPa/K), γ is a psychrometrcic coefficient, with typical value 0.67 hPa/K, and D is the vapor pressure deficit of the air (hPa), defined as the difference between the saturation vapor pressure ea and the actual vapor pressure es, which are functions of temperature and relative humidity. We remind that (2) estimates the evaporation rate (mass per unit area per day), which is expressed in terms of equivalent water depth by dividing by the water density ρ (1000 kg/m³). Next we will use symbols Ε΄ for evaporation rates, and E := Ε΄ / ρ for equivalent depths per unit time. In this context, FAO proposed the application of the Penman–Monteith method for the hypothetical reference crop, thus introducing the concept of reference evapotranspiration. With standardized height for wind speed, temperature and humidity measurements at 2.0 m and the crop height of 0.12 m, the aerodynamic and surface resistances become ra = 208 / u2 (where u2 is the wind velocity, in m/s) and rs = 70 s/m. The experts of FAO suggested using the Penman–Monteith method as the standard for reference evapotranspiration and advised on procedures for calculation of the various meteorological inputs and parameters [7].
Article
Full-text available
River basins are by definition temporally varying systems: changes are apparent at every temporal scale, in terms of changing meteorological inputs and catchment characteristics, respectively due to inherently uncertain natural processes and anthropogenic interventions. In an operational context, the ultimate goal of hydrological modelling is predicting responses of the basin under conditions that are similar or different from those observed in the past. Since water management studies require that anthropogenic effects are considered known and a long hypothetical period is simulated, the combined use of stochastic models, for generating the inputs, and deterministic models that also represent the human interventions in modified basins, is found to be a powerful approach for providing realistic and statistically consistent simulations (in terms of product moments and correlations, at multiple time scales, and long-term persistence). The proposed framework is investigated on the Ferson Creek basin (USA) that exhibits significantly growing urbanization during the last 30 years. Alternative deterministic modelling options include a lumped water balance model with one time-varying parameter and a semi-distributed scheme based on the concept of hydrological response units. Model inputs and errors are respectively represented through linear and non-linear stochastic models. The resulting nonlinear stochastic framework maximizes the exploitation of the existing information, by taking advantage of the calibration protocol used in this issue.
Article
Full-text available
A time series generator is presented, employing a robust three-level multivariate scheme for stochastic simulation of correlated processes. It preserves the essential statistical characteristics of historical data at three time scales (annual, monthly, daily), using a disaggregation approach. It also reproduces key properties of hydrometeorological and geophysical processes, namely the long-term persistence (Hurst–Kolmogorov behaviour), the periodicity and intermittency. Its efficiency is illustrated through two case studies in Greece. The first aims to generate monthly runoff and rainfall data at three reservoirs of the hydrosystem of Athens. The second involves the generation of daily rainfall for flood simulation at five rain gauges. In the first emphasis is given to long-term persistence – a dominant characteristic in the management of large-scale hydrosystems, comprising reservoirs with carry-over storage capacity. In the second we highlight to the consistent representation of intermittency and asymmetry of daily rainfall, and the distribution of annual daily maxima.
Article
Full-text available
Despite the great scientific and technological advances in flood hydrology, everyday engineering practices still follow simplistic approaches, such as the rational formula and the SCS-CN method combined with the unit hydrograph theory that are easy to formally implement in ungauged areas. In general, these "recipes" have been developed many decades ago, based on field data from few experimental catchments. However, many of them have been neither updated nor validated across all hydroclimatic and geomorphological conditions. This has an obvious impact on the quality and reliability of hydrological studies, and, consequently, on the safety and cost of the related flood protection works. Preliminary results, based on historical flood data from Cyprus and Greece, indicate that a substantial revision of many aspects of flood engineering procedures is required, including the regionalization formulas as well as the modelling concepts themselves. In order to provide a consistent design framework and to ensure realistic predictions of the flood risk (a key issue of the 2007/60/EU Directive) in ungauged basins, it is necessary to rethink the current engineering practices. In this vein, the collection of reliable hydrological data would be essential for re-evaluating the existing "recipes", taking into account local peculiarities, and for updating the modelling methodologies as needed.
Article
Full-text available
Koutsoyiannis, Demetris, 2011. Hurst-Kolmogorov Dynamics and Uncertainty. Journal of the American Water Resources Association (JAWRA) 47(3):481-495. DOI: 10.1111/j.1752-1688.2011.00543.x Abstract: The nonstatic, ever changing hydroclimatic processes are often described as nonstationary. However, revisiting the notions of stationarity and nonstationarity, defined within stochastics, suggests that claims of nonstationarity cannot stand unless the evolution in time of the statistical characteristics of the process is known in deterministic terms, particularly for the future. In reality, long-term deterministic predictions are difficult or impossible. Thus, change is not synonymous with nonstationarity, and even prominent change at a multitude of time scales, small and large, can be described satisfactorily by a stochastic approach admitting stationarity. This “novel” description does not depart from the 60- to 70-year-old pioneering works of Hurst on natural processes and of Kolmogorov on turbulence. Contrasting stationary with nonstationary has important implications in engineering and management. The stationary description with Hurst-Kolmogorov stochastic dynamics demonstrates that nonstationary and classical stationary descriptions underestimate the uncertainty. This is illustrated using examples of hydrometeorological time series, which show the consistency of the Hurst-Kolmogorov approach with reality. One example demonstrates the implementation of this framework in the planning and management of the water supply system of Athens, Greece, also in comparison with alternative nonstationary approaches, including a trend-based and a climate-model-based approach.
Article
This paper describes a methodology for calibration and uncertainty estimation of distributed models based on generalized likelihood measures. the GLUE procedure works with multiple sets of parameter values and allows that, within the limitations of a given model structure and errors in boundary conditions and field observations, different sets of values May, be equally likely as simulators of a catchment. Procedures for incorporating different types of observations into the calibration; Bayesian updating of likelihood values and evaluating the value of additional observations to the calibration process are described. the procedure is computationally intensive but has been implemented on a local parallel processing computer. the methodology is illustrated by an application of the Institute of Hydrology Distributed Model to data from the Gwy experimental catchment at Plynlimon, mid-Wales.
  • Konstantinos Papoulakos
Konstantinos Papoulakos et al. / Energy Procedia 00 (2017) 000-000