The objective of this study was to analyze the changes and uncertainties
related to water availability in the future (for the purposes of this study,
the period between 2011 and 2040 was adopted), using a stochastic approach,
taking as reference a climate projection from climate model Eta CPTEC/HadCM3.
The study was applied to the Ijuí River basin in the south of Brazil. The
set of methods adopted involved, among others, correcting the climatic
variables projected for the future, hydrological simulation using artificial
neural networks (ANNs) to define a number of monthly flows and stochastic
modeling to generate 1000 hydrological series with equal probability of
occurrence. A multiplicative type stochastic model was developed in which
monthly flow is the result of the product of four components: (i) long-term
trend component; (ii) cyclic or seasonal component; (iii) time-dependency
component; and (iv) random component. In general, the results showed a trend
to increased flows. The mean flow for a long period, for instance, presented
an alteration from 141.6 m
Discussions concerning variability and climate changes have intensified in the last few decades. Many studies have proved significant alterations in the composition of the atmosphere and in the concentration of gases that have implications for thermal energy, changing climate-related variables. On this topic the Intergovernmental Panel on Climate Change (IPCC) should be highlighted.
The IPCC was established in 1988 by the World Meteorological Organization (WMO) and by the United Nations Environment Program (UNEP). The objective is to supply scientific information in order to gain a better understanding of changes in the global climate, so as to evaluate their impact on society and on nature, and propose alternatives for adaptation and mitigation.
According to the IPCC (2013), it is already clear that the Earth has been warming since the beginning of the industrial period, as proved by the rise in the mean temperatures of the air and the oceans. Consequently, negative impacts have been observed as the increase in the mean level of the seas and the acceleration of ice melt in mountain or polar climate regions. Studies developed on a global scale have shown that several natural systems are already under the impact of climate changes.
Changes in temperature and precipitation will lead to an increased frequency of extreme meteorological events, such as severe floods and droughts, which will inevitably affect the availability of water for human consumption, irrigation, industries and other uses (IPCC, 2013). Some research studies on the sensitivity of agricultural crops to climate changes show that there may be a strong negative effect on crop growth, increasing the risk of losses in harvests worldwide (Mearns et al., 1996; Richter and Semenov, 2005; Zhang and Liu, 2005; Rasmussen et al., 2012).
The climate scenario projections are performed using global climate models (GCMs) and regional climate models (RCMs). The resolution of RCMs is between 10 and 50 km, which allows one to apply them in scenarios of climate changes in medium and small basins. Using these models, together with the GCMs, enables detailing of the climate processes at the local level, detecting the variations and specificities of a given region and thus improving the understanding of impacts in small basins (Marengo et al., 2009, 2012).
The Eta model was developed at Belgrade University and operationally implemented by the National Centers for Environmental Prediction (Black, 1994). The vertical coordinate system used in this model is recommended for use over South America due to the presence of the Andes mountain range (Marengo et al., 2012). Recently, a new version of the Eta model, Eta CPTEC, was developed independently by the National Institute for Space Research (INPE).
The regional Eta model was configured over South America and applied to downscale HadCM3 members of the Perturbed Physics Ensemble (PPE) experiment for the baseline (1961–1990). The dynamic downscaling method was used to generate the climate scenarios (Chou et al., 2012). According to Mujumdar and Kumar (2013), the main advantage of dynamical downscaling over the statistical downscale method is its ability to capture the mesoscale nonlinear effects. Furthermore, the dynamical downscaling provides information for many climate variables while ensuring internal consistency with respect to the physical principles in meteorology, simulating satisfactorily some regional climatic conditions.
The Eta CPTEC model includes the increase in CO
The study of Marengo et al. (2012) details the scenarios generated for South America using the Eta CPTEC/HadCM3 model. According to this study, the model is configured with 38 vertical layers, with the top of the model at 25 hPa. The Mellor–Yamada level 2.5 procedure (Mellor and Yamada, 1974) was used for the treatment of turbulence. The radiation package was developed by the Geophysical Fluid Dynamics Laboratory, based on studies by Fels and Schwarzkopf (1975) and Lacis and Hansen (1974). The Eta model uses the Betts–Miller (Betts and Miller, 1986) scheme modified by Janjic (1994) to parameterize deep and shallow cumulus convection and the Zhao scheme (Zhao et al., 1997) to parameterize cloud microphysics. This model also uses the NOAH scheme (Ek et al., 2003) to parameterize the land-surface transfer processes (Marengo et al., 2012).
Pesquero (2009), Chou et al. (2012) and Marengo et al. (2012) used model Eta CPTEC. In the first two studies, the model was used to reproduce the present climate in South America and to certify the quality of the model. A smooth tendency was observed to underestimate precipitation over the Amazon in the rainy season and the central region of Brazil, in the Brazilian savanna. In the last study (Marengo et al., 2012), model Eta CPTEC was used to study the climate changes in the Amazon, São Francisco and Paraná river basins between 2011 and 2100.
Currently, in the scientific literature, there are several studies that analyze the effects of climate changes on water availability (e.g., Kleinn et al., 2005; Hughes et al., 2011; Gunawardhana and Kazama, 2012). On a continental or global scale, normally, the outputs of the GCMs are used in combination with the empirical macroscale hydrological models that perform the water balance (for instance, Arnell, 1999, 2004; Nijssen et al., 2001; Milly et al., 2005; Nohara et al., 2006). The studies on water availability in smaller river basins normally use the climate projections for the RCMs, associated with empirical or physically based hydrological models, in a deterministic approach, offering only a single result in the hydrological sphere for each climate scenario. Examples of this are the studies by Middelkoop et al. (2001), Menzel and Bürger (2002) and Kleinn et al. (2005).
However, because of the randomness of hydrometeorological processes, the uncertainties related to climate modeling and future water availability favor the use of probabilistic methods based on stochastic time series, as in the studies by Wilks (1992), Semenov and Barrow (1997) and Booij (2005). The stochastic approach broadens the possibility of analyzing water availability and the climatic uncertainties in the future, offering a great number of scenarios for analysis. Thus, it is possible to identify the confidence intervals in the projection and to estimate the random component of the climatic and hydrological dynamics.
However, when generating hundreds or thousands of stochastic climate series, it is necessary to repeat the hydrological simulation often, rendering the modeling process very onerous from the computational standpoint. Moreover, in this approach the hydrological scenarios produced become even more sensitive to any imprecision in estimating the parameters of the rainfall-flow transformation model.
Location of the Ijuí River basin, section upstream from the
Santo Ângelo gauging station (5414 km
In order to minimize the processing time, this methodology will cover the randomness of the processes and the climate dynamics directly in the flow series, using a stochastic model appropriate for monthly flows. Thus, based on a single climate scenario, a flow series is generated by hydrological deterministic simulation and then the stochastic process is performed.
The objective of this study is to analyze the possible scenarios and uncertainties related to water availability in future, using a stochastic approach based on a climatic change scenario originating in the Eta CPTEC/HadCM3 climate model. This study will be applied to the Ijuí River basin, in Rio Grande do Sul (RS), Brazil.
The set of methods adopted in this study comprised the use of observed and simulated hydrometeorological data to analyze the uncertainties and possible scenarios of water availability in the future, based on scenario A1B of IPCC SRES, generated by regional climate model Eta CPTEC/HadCM3.
First, it is important to emphasize that the selection of the climate change scenario was made at the beginning of a research project (2010–2014). At that time, the new IPCC scenarios, for the AR5, were not yet available. Furthermore, all the data from climate model Eta CPTEC were provided by the National Institute for Space Research (INPE). This agency has recommended the use of the A1B scenario in four versions with different sensitivities. These versions were already being examined in large areas of the South American continent (e.g., Marengo et al., 2012). Therefore, given this context, the impacts of climate changes in medium and small river basins of Brazil were evaluated in more detail with the use of the A1B scenario.
For this study, considering the availability of the climatic data derived from regional climate model Eta CPTEC/HadCM3, the years between 1961 and 1990 were considered as the “base” period, and the years between 2011 and 2040 as the “future” period.
Simplifying, the methodological procedure covered (i) spatial interpolation of the meteorological variables; (ii) selection of the climatic scenario and correction of the climate variables; (iii) estimation of the potential evapotranspiration; (iv) hydrological simulation using artificial neural networks (ANNs); and (v) stochastic modeling of monthly flows to generate possible hydrological series in the future.
This study was applied in the Ijuí River basin, in the Santo Ângelo
stream gauging section, in the northwest of RS, Brazil. The basin area is
5414 km
The area of the study was chosen because the region depends to a great extent on agricultural activities and may suffer serious socioeconomic impacts from the climate changes. According to the State Coordinator of Civil Defense of RS, during the period between 1982 and 2011 there were at least six severe dry periods in the basin region. These dry periods caused great losses to the agricultural and cattle activities, mainly those involving soy beans and maize.
Considering the daily weather observations of the Cruz Alta station, operated
by INMET (National Institute of Meteorology), the winter and spring months
(from June to December) are the rainiest. According to Rossato (2011), the
annual rainfall is 1750 mm, which occurs within 110 days during the year.
The annual mean temperature oscillates between 17 and 20
The following materials were used in this study:
daily historical series of precipitations provided by the HidroWeb site
of the National Water Agency (ANA), during the period between 1961 and 1990,
at 77 rain gauging stations within the radius of coverage of 100 km of the
basin boundaries (Fig. 2); daily historical series of precipitation provided by IPH (Castro et al.,
1999), in the years 1989 and 1990, at 22 rain gauging stations (Fig. 2); daily historical series of precipitation, temperature, wind speed,
solar radiation, atmospheric pressure and relative humidity of the air
provided through the portal of BDMEP (Bank of Meteorological Data for
Teaching and Research) of INMET, during the period between 1961 and 1990, at
five meteorological stations (Fig. 2); daily historical series of flows from the Santo Ângelo station,
located at coordinates 28.36 daily data simulated by regional climate model Eta CPTEC, conducted
by four members of global climate model HadCM3, with different levels of
sensitivity (CNTRL, LOW, MID and HIGH), during the periods of 1961–1990
(“base”) and 2011–2040 (“future”). The variables simulated were
precipitation, temperature, wind speed, relative humidity of the air,
atmospheric pressure and solar radiation.
The first stage consisted of the spatial interpolation of the five daily climate variables (temperature, wind speed, relative humidity of the air, atmospheric pressure and solar radiation) and daily precipitation in the periods between 1961–1990 (observed and simulated data) and 2011–2040 (data simulated by the Eta model). The interpolation grid was generated with a spatial resolution of 5 km (Fig. 2), totalizing 264 nodes in the basin area. The interpolation procedure was performed for all data sets: (i) series observed at 104 rain gauging or meteorological stations; and (ii) series simulated using model Eta CPTEC/HadCM3 in four scenarios of climate sensitivity (CNTRL, LOW, MID and HIGH).
Location of the stations with hydrologic and climate data used in a radius of coverage of 100 km in relation to the Ijuí River basin.
The use of so many stations in a 100 km radius to begin the interpolation process consists of a safety margin, since many of these stations present short series, with many gaps. Thus, only on a few days when the stations closest to the interpolation grid present gaps, the method can select rainfall data from stations located slightly further away, in this way avoiding failures in estimating precipitation during the interpolation process. It can be said that for each day, in every node of the interpolation grid, only the closest stations with rainfall data were used, usually within the basin and immediate surroundings.
The interpolation method used was that of the natural neighbor (Sibson, 1981). This interpolation method obtained the best results in the study presented by Silva et al. (2013), with precipitation series similar to those used in the present study, also in the Ijuí River basin. In the study mentioned, the following methods were also tested: closest neighbor, linear triangulation and inverse distance weighting.
The natural neighbor method is based on the concept of area of influence of the sampling points determined by Voronoi polygons. These polygons are obtained from the Delaunay triangulation. For each point on the interpolation grid, the weight of each sampling point is calculated because of the area of influence. The daily value of each variable in the basin was obtained from the mean of the values interpolated in all nodes of the regular grid.
Still at this stage, the daily mean value of the five climate variables and of precipitation in the Ijuí River basin was calculated, considering the data observed and the data simulated by the ETA model. Finally, the monthly accumulated precipitation for the observed series and for scenarios simulated by the Eta model in the periods of 1961–1990 (base) and 2011–2040 (future) were calculated.
The outputs of climate models should not be used directly to estimate future water availability (Graham, 2000). The climate models may not represent perfectly the current climate due mainly to the influence of the spatial discretization of the models. It is observed (Lenderink et al., 2007) that the outputs may present systematic errors. The correction of climate variables is intended to prevent the errors intrinsic to the output of the climate models being propagated to the subsequent hydrologic modeling.
Recently several techniques to correct the climate variables resulting from the GCMs and RCMs were developed and compared (Themeßl et al., 2012). The use of disturbances (Delta change approach) in climate variables is a commonly used strategy to simulate the impacts of climate changes, obtained via global or regional climate models of water resources (Graham, 2004; Lenderink et al., 2007). The technique consists of using only the seasonal change foreseen between the current and future scenario, obtained with the climate model. This change is represented by the difference between the current climatic conditions and those foreseen for the future, both conditions obtained by the climate model. The change foreseen is incorporated into the historical series of precipitations and temperature to generate the series in the future. Thus the error associated with climate modeling is eliminated from the current conditions, and becomes limited to the uncertainties associated with the forecast of climate changes for the future. Examples of applying this methodology are the studies by Kaczmarek et al. (1996), Lettenmaier et al. (1999), Graham (2000) and Bergström et al. (2001).
However, as mentioned by the authors themselves (Graham, 2000; Bergström et al., 2001), and supported by Lenderink et al. (2007), applying the forecast changes in temperature or in precipitation directly to the series observed implies considerable simplifications that may compromise the analysis of the projections in future. In this approach, for instance, probable changes in the number of rainy days, in dispersion (variance) of rains or in the extreme values of temperature are not considered. This occurs because the series itself observed in the past consists of the base of forecasts for the future, and only the seasonal mean variations are taken into account. In this case, there is a risk of considering that the same anomalies recorded in the past will be observed in the future with small changes in the monthly magnitude of climate variables, according to time of the year.
Thus, Lenderink et al. (2007) discuss and analyze how the output of a regional climate model should be corrected to obtain more realistic flows for the current climate and, consequently, for the future climate. According to the authors, the development of a regional climate model, with some corrections in the output, allows the direct approach in using projections of temperature and rainfall for the future. This method, instead of adding the changes forecast in the series observed, performs a different procedure: (i) it detects the differences between the current climatic conditions, i.e., between the conditions observed using meteorological stations and the conditions simulated by the regional climate model; and (ii) it applies these differences in the series forecast for the future.
Other more sophisticated methods have been tested and compared, with applications at daily or monthly time intervals, as can be seen in Wood et al. (2004), Maurer and Hidalgo (2008), Boé et al. (2007), Piani et al. (2010) and Bárdossy and Pegram (2011). In a recent study, Themeßl et al. (2011) compared a few correction methods and concluded that the quantile-based mapping technique (Panofsky and Brier, 1968) is the most effective one to remove the errors in the precipitation data. This method is applied with small adaptations in the studies listed above. Essentially, the method is based on the differences between the accumulated probability curves (simulated and observed) of daily or monthly precipitations.
In the study by Oliveira et al. (2015a), whose objective was to evaluate the climatic conditions simulated using model Eta CPTEC/HadCM3, emphasizing the study of water availability in the Ijuí River basin, four methods to correct the climate variables were tested: (i) Delta change approach, (ii) direct approach, (iii) monthly quantile-based, and (iv) quarterly quantile-based. The control period in which the corrections were applied and the hydrological model calibrated was defined between 1961 and 1975. The evaluation period, in which the results of the climate scenarios and water availability were found, was 1976 to 1990. For both periods, data were available that had been observed at rain gauging stations and meteorological stations and data simulated by regional climate model Eta CPTEC, conducted by four members of global climate model HadCM3, with different levels of sensitivity.
The main results obtained in Oliveira et al. (2015a) were the following: (i) only Eta HIGH did not prove satisfactory in most of the aspects analyzed regarding precipitation, evapotranspiration, and flow; (ii) in evaluating the flows resulting from the hydrologic modeling process, the Eta LOW member was outstanding, especially as regards the mean monthly flows (mean error of 22.6 %), the annual flow permanence curves (mean error 12.6 %) and the quarterly flow permanence curves (mean error 27.3 %); (iii) with Eta LOW, a good adjustment can be seen, both to the low flows (permanence greater than 90 %) and to the high flows (permanence less than 10 %); (iv) the outstanding climate scenario was Eta LOW, applying the direct approach correction method, especially as to the curve of permanence of the flows; and (v) finally, it was pointed out that in the case of the precipitations and flows, the difference between simulated values, based on the Eta model and the values observed, was greater than those of evapotranspiration, resulting in errors that were sometimes greater than 20 %. One should, therefore, consider that these uncertainties will be reproduced in future scenarios (for the coming decades of the 21st century).
Since the present study focuses on a stochastic approach that takes into account the uncertainties associated with the various stages that comprise the modeling of water availability in future, it was necessary to adopt a climate scenario to test the methodology. Thus, taking into account the results obtained in Oliveira et al. (2015a), the use of the Eta LOW member was defined, applying the direct approach correction method.
In the direct approach method used by Lenderink et al. (2007), the
precipitation that is corrected in the future period (2011–2040), in
month
The other five climatic variables (temperature, wind speed, relative humidity
of the air, atmospheric pressure and solar radiation) were corrected in the
daily time interval, using the direct approach, as shown in Eq. (2).
In the third stage the (daily) reference evapotranspiration was calculated
for the simulated and corrected climate scenario and for the observed series
in the base (1961–1990) and future (2011–2040) periods. The reference
evapotranspiration was calculated using the Penman–Monteith method (Penman,
1948; Monteith, 1965), which has been considered the most reliable method by
some authors and was adopted as the standard method by the United National
Food and Agriculture Organization (FAO) (Allen et al., 1998). This method is
parameterized for an area completely covered with 12 cm high grass,
considering the aerodynamic resistance of the surface of 70 s m
After calculating the daily evapotranspiration, these values were converted to the monthly time interval, rendering it compatible with the monthly accumulated precipitation series for hydrological modeling.
Recently, several studies have obtained excellent results applying ANNs in the field of water resources and hydrology, especially in the development of models for simulation, forecasting and classification (Bowden et al., 2005; Jain and Kumar, 2007; Leahy et al., 2008).
The methodology adopted in this study comprised the use of a hydrological
model based on ANNs, consisting of transformations of the meteorological and
pluviometric variables. The program for the necessary implementation was
developed in the MATLAB R2010a environment, consisting mainly of a
generalized model, constituted by linear transformations of inputs and
outputs from a neural network with a hidden layer (Eq. 3).
The choice of a three-layer architecture was based on the Kolmogorov mapping
neural network existence theorem (Hecht-Nielsen, 1987), which stated that any
continuous function with
The ANN is the model core and is represented by Eq. (4):
The activation function used, both for the hidden layer and for the external
layer, was the unpolar sigmoid, with outputs at the interval [0, 1], whose
derivate can be calculated only as a function of the output, and they are
represented by Eqs. (5) and (6).
The network training was performed through the back-propagation algorithm
with crossed validation. This algorithm was proposed by Rumelhart et
al. (1986), and consists of a method of searching for the synaptic weights to
minimize errors, using the so-called Delta rule (Widrow and Hoff, 1960),
Eq. (7), which was formulated initially for one-layer neural networks.
In order to apply this method to neural networks with more layers, Eq. (8)
is used to estimate the errors in the hidden layers (h), which depend only
on the errors and properties of the subsequent layers (s):
The ANN hydrological model used was performed in the study of Oliveira et al. (2014), and resulted in the application of an algorithm for simplification of the neural network (Oliveira et al., 2015b). The reduction of input variables and neurons in the internal layer was performed using an algorithm that looks at the model performance after the imposition of small disturbances in the ANN input data.
The initial ANN model was composed of ten input variables, which included
precipitation and evapotranspiration values at times
According to Salas et al. (1980), if a variable cannot be predicted with certainty, it can be considered a random variable, ruled by the laws of probability. A model can be defined as stochastic when at least one of the variables involved presents random behavior. According to Salas et al. (1980), the climatic and hydrological variables can be considered random and thus modeled stochastically. In the scientific literature there are numerous references involving the development of stochastic models to generate synthetic climatic and hydrological series (Gabriel and Neumann, 1962; Thomas and Fiering, 1962; Bailey, 1964; Richardson, 1981; Semenov and Barrow, 1997).
In this study, a multiplicative type stochastic model was developed to
generate monthly flow series. A preliminary analysis of monthly hydrological
series was performed to examine the stationarity, seasonality and the
temporal dependence. Based on this analysis, for this model, the assumption
was adopted that flow may be estimated by the result of the product of four
components that must be estimated in the following sequence: (i) component of
long period tendency (C1) that depends on the position in time, month (
The product of the four components (Eq. 11), during all the time intervals
of modeling, results in a stochastic sequence of monthly flows (
In order to isolate and remove the tendency observed in the series of monthly
mean flows during the base period (1961–1990), a linear tendency function
was adjusted, represented by Eq. (12), that calculates flow based only on the
time interval (
Then the time dependency component was modeled (C3), which represents the
influence of the stream values of the
Cyclic (seasonal) component in the base and future periods: mean monthly flow in the Ijuí River basin, Santo Ângelo station.
In the multiplicative model, component C3 is a non-dimensional factor, with
a mean equal to 1 along the hydrological series, obtained by the ratio
between observed flow (stationary), in month
The random component (C4) is defined as the part that is not explained by the
three other deterministic components, i.e., that represents the changes in
hydrological behavior provoked by extreme events that occurred in the month.
This part of the monthly flow is represented by the ratio between stationary
flow (month,
The most marked oscillations (inflections or impulses) in the monthly hydrogram, which depend on the random component C4, occur predominantly in dry periods, when the flow is below the mean observed for the month. This pattern observed in the historical series explains the smooth tendency found in the values of this component.
Also, considering the stationary series of the future period (2011–2040), when the value of C3 was higher than 1 (high flow periods), the random component C4 presented less dispersed values, ranging from 0.24 to 2.46, with a slightly lower mean (0.99). On the other hand, when the value of C3 was less than 1 (dry periods), component C4 oscillated between 0.13 and 4.98, with a mean of 1.06.
Once the probability curves observed in both periods (base and future) had
been observed, a few statistical distributions were adjusted (Gamma,
log-normal, Weibull, among others) to the values of the random component C4.
After the Kolmogorov–Smirnov adherence test was performed, it was found that
the Gamma probability distribution with three parameters presented the best
adjustment to the component modeled. The Gamma distribution with three
parameters (
After the adjustment of the four components, the stochastic series for both periods were generated, referenced to the parameters calculated based on the two monthly flow series (observed between 1961 and 1990, and simulated between 2011 and 2040). One-thousand series with an equal probability of occurrence were generated for each period.
Curves of volume discharged in the future (2011–2040) – difference between the original series (simulated) and the 1000 stochastic series generated – Ijuí River basin, Santo Ângelo gauge station.
Difference between the original series (simulated) and the 1000 stochastic series generated – mean flow and monthly standard deviation in the period between 2011 and 2040, Santo Ângelo gauge station.
The stochastic modeling process was evaluated by comparing the series generated and the series simulated in the future period, from the following aspects: (i) mean monthly flows; (ii) long period mean flow and volume discharged; (iii) standard deviation of monthly flows; and (iv) permanence curves.
The changes and uncertainties in water behavior were evaluated by comparing the stochastic series generated for the future period (2011–2040) and the series generated for the base period (1961–1990), considering central values and limits of confidence, looking at the following aspects: (i) mean monthly flows; (ii) standard deviation of monthly flows; (iii) long period mean flow and volume discharged; and (iv) permanence curves.
This section will present the results and the discussions held concerning the analysis of stochastic modeling of monthly flows and the changes and uncertainties in water availability in the future period, between 2011 and 2040.
The stochastic series generated preserved several characteristics of the
original series, simulated for the period between 2011 and 2040. Considering
the mean of the 1000 series generated for the future period, the long
period mean flow (LPMF) was 200.3 m
Another characteristic maintained from the original series was the mean
monthly flow. Table 2 shows that the mean absolute difference was only
0.52 %, considering the mean of the 1000 series generated for the period
between 2011 and 2040. The greatest absolute difference between mean flows
occurred in October, with an overestimation of 1.6 m
Table 2 also shows that the monthly standard deviation was reasonably preserved, with a mean percentage absolute difference of 13.9 % between the original series and the central tendency of the 1000 series generated. The smallest difference was found in the month of October, and the greatest difference as to the monthly standard deviation was found in the month of May.
Figure 4 illustrates the permanence curves of the mean monthly flow in the future period (2011–2040), in which the similarity between the original series and the central tendency observed in the stochastic series generated becomes clear. The greatest differences were observed in the extremely high flows, with a permanence of less than 2 %. In the rest of the permanence intervals, the original curve was always located at the 90 % confidence interval defined by the red lines on the graph.
In the Ijuí River basin, according to the climate scenario used, the annual accumulated rainfall will increase by 12.3 % between 2011 and 2040. This growth in volume of rainfall is mainly due to an increasing trend in rainfall between the months of January and June.
Permanence curves for the mean monthly flow between 2011 and 2040 – difference between the original series (simulated) and the 1000 stochastic series generated – Santo Ângelo gauge station.
Mean and 90 % confidence interval for the volume discharged, based on the stochastic series generated, base period (1961–1990) and future period (2011–2040), Santo Ângelo gauge station.
On the other hand, the evapotranspiration will decrease by 5.4 %, based on the annual average. According to the climate scenario used, this reduction in the evapotranspiration should be observed in almost every month, even though the average temperature is higher in the period 2011–2040. The reason for this reduction is associated with the increase in relative humidity and the decrease in solar radiation, probably associated with the increase in cloudiness. This statement was confirmed by analyzing the changes related to the five climatic variables used to calculate evapotranspiration.
The first aspect analyzed as to changes and uncertainties regarding water
availability in the future refers to the long period mean flow (LPMF) and to
the volume discharged over the period of 30 years. On average, considering
the stochastic series in the base period (1961–1990), the LPMF was
41.6 m
The change of LPMF according to the projection for the future is also
reflected by the mean of the total volume discharged over a 30-year period.
Figure 5 shows that, between the years of 1961 and 1990, the mean of the
total volume discharged was 132 566 Hm
Considering the stochastic series in the future period, at a 0.1 level of
significance, Fig. 5 shows that the total volume discharged at the end of
30 years is at the interval between 154 014 and 218 002 Hm
The second aspect analyzed refers to mean monthly flows. Figure 6 presents the mean and the 90 % confidence interval for the mean monthly flows, considering the 1000 stochastic series generated during the base and future periods.
Mean and 90 % confidence interval for the mean monthly flows based on the stochastic series generated, during the base (1961–1990) and future periods (2011–2040), at Santo Ângelo gauge station.
The mean monthly flow will increase between the months of January and
October, during the period between 2011 and 2040, compared to the base
period, with percentages that vary from 15 % (August) to 118 % (March).
Besides the month of March, at least four other months will present a
significant increase in mean flow: (i) February (113 %); (ii) May
(110 %); (iii) April (101 %); and (iv) June (74 %). Considering a
simple difference between the values obtained in the two periods, the months
of May and June presented the greatest changes, with an increased mean
monthly flow of 130 and 118 m
Considering a statistical analysis of the 1000 stochastic series generated for the two periods analyzed (base and future), at a 0.1 level of significance the confidence interval can be estimated that comprises the mean flow of each month. The greater the range of this interval, the greater also the uncertainty related to the mean monthly flow.
Figure 6 shows that the range of the 90 % confidence interval for the mean
monthly flows will only be reduced in the months of November and December,
thus following the tendency observed in the mean monthly values. In
November, for instance, the range of mean flow in the base period
considering the series generated was 75 m
In all other months, the range of the confidence interval increased in the
future, particularly between the months of February and June, with a greater
percentage than 100 %, indicating greater variability between the
stochastic series generated and, consequently, greater uncertainties in
estimating mean flow. The month of May presented the greatest change in this
sense. The mean flow during the base period, considering a 90 % confidence
interval, was between 95 and 145 m
Mean of standard deviation of monthly flows during the base and future periods – Santo Ângelo gauge station.
All the results of mean monthly flows presented indicate a significant change in the hydrological behavior of the Ijuí River basin, considering the climatic projection of the Eta model, between the months of February and June. Between the months of February and June, the confidence intervals do not present any overlap; i.e., the upper limit of the interval found in the base period is smaller than the lower limit of the interval found in the future.
The third aspect analyzed in the hydrological comparison between the base (1961–1990) and future (2011–2040) periods was the standard deviation of mean monthly flows. As in the case of the averages of the flows in each month, considering the central tendency of the 1000 series generated in the two periods, Table 3 illustrates that the standard deviation should increase between the months of January and October.
The period of the year between the months of February and July is that one
where the greatest change occurs in the dispersion of the flow values.
Table 3 shows that in May, for instance, the standard deviation increases
155 % for the future. On the other hand, the month of November presents a
smooth tendency to reduction in the flows, with a 121 m
When dividing the monthly standard deviation by the mean monthly flow, the coefficients of variation (CV) were obtained for both series, for each month. It can be seen that during the base period (1961–1990), the CV oscillated between 0.7 (February) and 0.72 (November), while in the future period (2011–2040), the same index varied between 0.8 (April) and 0.85 (May). These results indicate a real increase in the monthly variability of flows, with greater fluctuations of monthly flows in the future.
Another aspect analyzed as to changes in hydrological behavior in the future refers to permanence curves of mean monthly flows. Figures 7 and 8, respectively, illustrate the mean value and confidence interval of 90 % for the permanence curves of monthly flow, considering the 1000 stochastic series generated in the base (1961–1990) and future periods (2011–2040).
Flows with probability of exceedance equal to or over 90 % (
Mean value of permanence curves of monthly flow according to the stochastic series generated during the base (1961–1990) and future periods (2011–2040), at Santo Ângelo gauge station.
90 % confidence interval for the monthly flow permanence curves, according to the stochastic series generated in the base (1961–1990) and future periods (2011–2040), at Santo Ângelo gauge station.
The flow will be reduced in the future period only at permanence intervals
greater than 91 %, i.e., in the portion of lower flows that characterize
dry periods. For flows with a permanence equal to or less than
On average, considering all the series generated during the base and future
periods, flow with a probability of exceedance equal to or less than 99 %
of the months (
On average, considering all the series generated during the base (1961–1990)
and future (2011–2040) periods, flow with a probability of exceedance equal
to or less than 95 % of the months (
Mean and 90 % confidence interval for the monthly flow permanence curves at Santo Ângelo gauge station, according to the stochastic series generated in the base period (1961–1990) and future period (2011–2040): January, February, March and April.
In the base and future periods, the mean flow with a probability of
exceedance equal to or less than 90 % of the months (
In the base period (1961–1990), on average, the flow with a probability of
exceedance equal to or less than 50 % of the months (
Mean and 90 % confidence interval for the monthly flow permanence curves at Santo Ângelo gauge station, according to the stochastic series generated in the base period (1961–1990) and future period (2011–2040): May, June, July and August.
Mean and 90 % confidence interval for the monthly flow permanence curves at Santo Ângelo gauge station, according to the stochastic series generated in the base period (1961–1990) and future period (2011–2040): September, October, November and December.
In the portion of flows with permanence between 5 % (
Finally, the changes in the permanence curves of the mean monthly flows in
the future, individually, for each month were analyzed. Comparing the
permanence curves in the two periods – base (1961–1990) and future
(2011–2040) – it can be seen that the smallest changes observed occurred
between August and January. In December the absolute mean difference between
the permanence curves was 26 m
Figures 9–11 illustrate the mean behavior and the 90 % confidence interval
for the permanence curves of the monthly flows from January to December, for
both periods (base and future). In general, it can be said, based on the
results obtained, that between the months of January and October there is a
tendency for the value of the flows with low permanence to increase – the
high flow portion. Regarding this aspect, the main outstanding month is May,
in which the mean flow with permanence equal to or less than 10 %
(
Table 4 shows that between the months of February and June, the flows with a
high permanence (portion of the lower flows) also presented higher values in
the future period compared to the base period, indicating a tendency to a
more generalized increase in the flows for these months. In this case, in
percentage terms, the month of March is outstanding, in which the mean flow
with a probability of exceedance equal to or inferior to 90 % (
Mean flows (m
On the other hand, in the months of January, July, August, September and
October, even lower flow values were observed, with high permanence (low
flows) indicating that in those months there was a tendency to amplify the
extreme values: dry periods and more intense floods in the future period
(2011–2040) than those observed in the base period (1961–1990). In January,
for instance, the results indicate a mean increase of 47 % in
In the months of November and December, the tendency observed is for a
reduction in the flow values in general, both in the high flow portion and
in the low flow portion. As shown in Table 4, in November the results
indicate a mean reduction of 18 % (
Tables 5 and 6 show the limits and ranges of the confidence interval of
flows during the base and future periods, with a permanence of 10 % (
In May, for instance, considering a level of significance of 0.1, the
In general, the uncertainties regarding the hydrological behavior in the future (2011–2040), taking a single climate scenario as reference, were greater than during the base period (1961–1990). This increase was reflected mainly between the months of January and October, as shown by the results of the comparative analysis between the permanence curves and the mean month flows and their confidence intervals.
Limits and ranges of the confidence interval of flows
(m
Limits and ranges of the confidence interval of flows
(m
The primary source of uncertainties is in the original hydrological series itself, used in the stochastic modeling process. By formulating the stochastic model it is expected that the greater the mean monthly flow (seasonal component, C2), the greater also will be the possibility of obtaining extremely high flows. This occurs because the seasonal component is multiplied by the random component (C4) and the time dependence on (C3), which, although they have mean volumes close to 1, may possibly present extreme values.
This becomes clear when compared to the mean monthly flow of each month (in the input series to the stochastic model), with the range of the confidence interval for the mean monthly flow obtained after modeling, as shown in Fig. 12. There is a visible linear tendency to increased uncertainty as the mean monthly flow increases. However, a clear difference is also observed between the two straight lines that characterize the base and future periods. For the same mean monthly flow, the confidence interval range is higher in the future period series.
After a sensitivity analysis in the models based on ANN to determine the C3
component (time dependency) in both periods, it was found that in the future
(2011–2040) the flow in time
In the base period, between 1961 and 1990, even when an extremely low flow
occurs in the previous month resulting in a value close to 0 for variable
C3(
Relationship between the mean of the monthly flow and the range of the confidence interval for the periods between 1961 and 1990 (base) and between 2011 and 2040 (future).
Variation of the value of C3(
The same pattern was observed for the portion of the extremely high flows.
During the period between 1961 and 1990, when there is a high flow in the
previous months, resulting in a value of C3(
Adjustment of the Gamma distribution for the modeling of the
random component in a low flow situation, C3(
Adjustment of the Gamma distribution for the modeling of the
random component in a high flow situation, C3(
In this way the component C3 presents greater fluctuations in the series between 2011 and 2040. This result helps explain the greater variability found between the stochastic series of the future period in relation to the base period.
Figures 14 and 15 illustrate the adjustment in the distribution of Gamma
probabilities for modeling the random component (C4) in situations of low
flow (C3, in time
In general, it is possible to observe that the behavior found in the base series (1961–1990) of the random component C4 was maintained in the series of the future period (2011–2040), especially as regards the months in which the value of C3 was less than 1 (Fig. 14), resulting in a flow lower than the monthly mean. In this case, considering the base and future periods, the chance of the value drawn for C4 being greater than 1 was 42 and 43.5 %, respectively.
On the other hand, in the months when the time dependence component (C3) surpassed the value of 1, the difference between the series was slightly higher (Fig. 15). The probability of a value higher than 1 being drawn for component C4 was 38 and 43 %, respectively, for the base and future series.
These results indicate that the sensitivity of the model to the variable of
time dependence also contributed to increasing the uncertainties in the
future period, between 2011 and 2040. In the original series simulated for
the future period, besides the mean and the dispersion of the data being
greater than in the base period, provoking more abrupt fluctuations in the
flow values, the correlation coefficient between the flows at times
Considering the methodology adopted to model flows in future and to generate the stochastic series, it can therefore be said that there is a certain tendency to an increased hydrological variability during the period between 2011 and 2040, with a greater dispersion of values in relation to the monthly mean. This finding implies greater uncertainty regarding the availability of water in the future, with the possible occurrence of time series that are very different from each other.
This study analyzed the possible changes and uncertainties related to water availability in the future using a stochastic approach, based on the climate change scenario originating in the LOW member of the Eta CPTEC/HadCM3 climate model, for the period between 2011 and 2040. The study was applied to the Ijuí River basin, in the south of Brazil. The methodology involved the correction of the climate variables projected for the future, the hydrological simulation to define a series of monthly flows, and stochastic modeling to generate 1000 hydrological series with an equal probability of occurrence.
As to the stochastic model to generate monthly flow series, several characteristics of the original series were preserved, simulated for the period between 2011 and 2040. Outstanding among them are LPMF and the mean monthly flows, both with differences of only 0.5 %. The monthly standard deviation was reasonably preserved, with a mean percentage absolute difference of 13.9 % between the original series and the central tendency of the 1000 series generated. The similarities between the permanence curves of the monthly flows of the original series and the central tendency observed in the stochastic series generated also became clear. Based on all these results it can be concluded that the stochastic model proposed is adequate to generate monthly flow series.
Various results showed a tendency to increased flows in a general context.
The LPMF, for instance, presented an alteration from 141.6 m
Based on the comparison of the permanence curves of monthly flow between the
base and future periods, it is concluded that the flow presented lower
values (
It can also be observed that the smaller changes in flow permanence occurred
between the months of August and January. On the other hand, in the other
months, the changes were drastic. In May, for instance, an absolute mean
difference was found of 130.5 m
In general it is concluded, based on the results obtained, that between the months of January and October there is a tendency for the flood flows to increase. Between the months of February and June, the flows with high permanence (minimum flows) also presented higher values in the future compared to the base period. On the other hand, in the months of January, July, August, September and October, even lower minimum flow values were observed, indicating that in these months there is a tendency to amplify the extreme values. Finally, in the months of November and December, the tendency observed is for the reduction of flow values, in general, both in the high flow and in the low flow portions.
As to the uncertainties concerning the hydrological behavior and, consequently, water availability for the future, having as a reference the results and discussions presented, it is concluded that uncertainties regarding hydrological behavior between 2011 and 2040 were greater than in the base period. The main factor that contributed to this result was the increase in the mean itself and in the standard deviation of monthly flows. Besides these, in the future, time dependency will present a more marked contribution to the composition of monthly flow, making the model more sensitive to abrupt variation in flow the previous month.
In this way, considering the stochastic series generated for the future, it can be said that there is a certain tendency for the increased hydrological variability during the period between 2011 and 2040. This finding means greater uncertainty regarding water availability in the future, with the possibility that time series may occur with marked differences as to the occurrence of drought and flood periods.
We are grateful to FINEP for funding the research – MCT/FINEP CT-HIDRO 01/2010 – Convênio 01.12.0396.00, project Research Network in Monitoring and Modeling Hydrosedimentological Processes in Representative Rural and Urban Basins of the Atlantic Forest Biome (RHIMA). We thank CNPq for the doctoral scholarship of the first author of this study and for the Research Productivity Grant for the third author. Edited by: A. Opere