Study area

The study area encompasses the Ñuble River Basin, which contains 38.6% of the total area of the region where it is located. Its main economic activities are agriculture and silviculture (^{DGA, 2004b}), and it is here where the 12th most populated city in Chile is found (about 200,000 inhabitants), the city of Chillan (^{MINVU, 2002}). It is located between coordinates 36.29°S and 37.33°S and between 71°W and 72.46°W, in the Ñuble region, in south-central Chile (Figure 1).

Figure 1 Study Area Ñuble River Basin, sub-basins and control points. The sub-basins are shown with grey tones and are labelled using the name of the corresponding river. 

The Ñuble River, with a length of 155km, has a basin area of 5097 km² (^{DGA, 2004b}).

The eastern part of the study area is situated in the Andes mountain, and the western part in the central valley, which is a strip in the Chilean topography that, due to its extension and as a continuous relatively flat area, facilitates the settlement of a great part of the population (^{Universidad de Chile, n.d.}).

This basin, influenced by a Mediterranean climate, presents at least two consecutive months of summer with hydrological deficit, a period in which there is higher demand for water resources. In 1991, the basin presented a total of 1119 canals, which served for the irrigation of 562 km², equivalent to 11% of its total surface area (^{DGA, 2004b}).

The area of study was divided into seven control points where water availability was determined: the mouths of the Cato, Chillan, Changaral, and Ñuble rivers (D, E, F y G in Figure 1), in addition to three additional points of interest in the Ñuble River (A, B y C in Figure 1). The points situated at the outlets were selected because they are the most influential affluents (^{DGA, 2004b}); the points in the Ñuble River were chosen because they present Water Rights with conceded flows of great magnitude in its contributing sub-basins.

Water availability evaluation

For the evaluation, a balance between demand and supply of water must be conducted, which results in the availability of flow for the constitution of new Water Rights in the evaluated points (^{DGA, 2008}). This was evaluated for the Water rights of permanent use and those of non-regular use. On the one hand, the article 17th of the Chilean water code (DFL, 2018) states that permanent use rights “are those that allow the use of water in a corresponding amount.” On the other hand, article 18th mentions Water rights of non-regular use as those that “only allow the use of water in periods in which the main flow presents a residual after the permanent use rights are met”.

Water surplus

To conduct the availability analysis it is necessary to estimate the superficial resources in a natural regime (^{DGA, 2004a}), meaning that it must be considered the flow pass through the point assuming there is no human extraction or intervention.

For this purpose, the method of basin transposition by area and precipitation was applied, since this procedure is the one recommended by the manual of norms and procedures for the administration of water resources of the DGA (Dirección General de Aguas). Although not new, this method is highly recommended and adequate for the goals of this work. This is a widely used methodology to determine flows in non-instrumented basins (^{Álvarez-Sevilla, Brown-Manrique, & del Cid-Colindres, 2017}; ^{Duitama, Moreno, & Zamudio, 2015}), where other methods, such as the flow-precipitation correlation or the water balance are impossible to apply due to lack of data. In effect, this methodology estimates the flow in a natural regimen that would pass through a point evaluated using records of reference gauging stations. Reference stations selected for the present study correspond to those that, due to their closeness to points in evaluation, present similarities in regime and that practically do not undergo water extractions in their contributing sub-basins, allowing calculation of the theoretical flows that would pass through the evaluated points. This method assumes that the evaluated point has the same flow regime as the reference station, and that the relation is established according to the size of the sub-basin that it conforms and its average annual precipitation. The equation that describes that calculation is the following:

Where qij: standard monthly flow estimated for a month i and probability for excedence j; Qij: median monthly flow of the reference flow for a month i and a PE j; a: drained area of the evaluated catchment; p: median annual precipitation of the evaluated catchment; A: drained area of the reference catchment; P: median annual precipitation of the reference catchment. To estimate the a parameter for each sub-basin of the Ñuble River, the limits of the Ñuble River Basin and its sub-basins were determined using the ArcHydro tools of the ArcGIS software (^{ESRI, 2011}). The topographic database used for this procedure was the digital elevation model SRTM, with a spatial resolution of 1 arc second. This model was downloaded from the Earth Explorer web platform of the U.S. Geological Survey (^{USGS, 2014}). The downloaded product was processed with the precipitation and flow calculations detailed in the following sections.

The application of equation 1 yields the water surplus, the average monthly flows in natural regimen at Q10PE, at Q85PE and at Q95PE, of each evaluated point, i.e. 10%, 85%, and 95% probability of exceedance respectively.

Reference gauging stations

Based on the ^{DGA (2004b)} study, two stations showing a regime close to natural one were used for the analysis, with a regimen close to the natural one, and were obtained from the National Water Bank (^{DGA, 2017a}): (a) Sauces station, for mountain sub-basins, with a mixed regime (A, B, C y G in Figure 2), and (b) Cholguán station, to determine the availability in the sub-basins with pluvial regime (D, E, F y G in Figure 2). These cases were considered to be in natural regime because there are no flow extractions upstream these stations.

Figure 2 Stations, points and regimens in the study area. In the main panel the localization of the standard basins of the Cholguán and Sauces creeks in relation to the Ñuble River Basin can be seen. The side panels identify the sub-basins associated with each control point. 

A special case occurs in G at the Ñuble River mouth, since it has a pluvial and mixed (pluvio-nival) regime (Table 2 and Figure 2). Due to this, this point utilized both reference stations. The zone of mixed regimen of point G was considered as the sub-basin of point C, which used station Sauces as reference. The rest of the basin was considered a zone of pluvial regime, using Cholguán station as reference.

Table 2 Coordinates and regime of gauging stations and locations evaluated in this study. Source: This study based on data from ^{DGA (2004)} and ^{DGA (2017a)}. 

ID		Location	Coordinates		Elevation (masl)	Regime
			S	W
Reference station	Sauces	Confluence Sauces and Ñuble Rivers	36.666°	71.274°	700	Mixed
	Cholguán	Río Itata at Cholguán	37.157°	72.068°	225	Pluvial
Location evaluated	A	Upper Ñuble	36.664°	71.322°	655	Mixed
	B	Mid Ñuble	36.483°	71.737°	288	Mixed
	C	Mid Ñuble	36.519°	71.902°	191	Mixed
	D	Cato River mouth	36.552°	72.086°	114	Pluvial
	E	Chillan River mouth	36.601°	72.332°	53	Pluvial
	F	Changaral River mouth	36.601°	72.344°	49	Pluvial
	G	Ñuble River mouth	36.643°	72.462°	27	Mixed/Pluvial

The time series of the monthly average flows of the last 25 years were used, from the hydrologic year of 1991-92 until 2016-17. The first year of the study period was selected because the El Niño phenomenon was not extreme that year according to data from ^{NOAA (2018)}.

Probabilities of exceedance (PE) for each month were obtained using the FRECwin statistical analysis software, which determines PE for five flow frequency distributions (Weibull, Normal, Log- Normal, Gumbel, Gamma) employing the chi square test, to determine the best fit for each case, obtaining the monthly Q10PE, Q85PE and Q95PE average flows (^{DGA, 2004a}).

Water demand

For the calculation of water demand, the water rights in the study area were analyzed, since the available flow depends on the difference between the existing flow in the river minus the rights that must be respected, considering the environmental demand (^{DGA, 2008}).

An analysis of the available water rights records in the public water cadaster until 2017 was conducted (^{DGA, 2017b}: ^{DGA, 2008}), in conjunction with records from the internal database of the Water Resource Information Center (CIRH). The records of the CIRH correspond to requested, but not necessarily constituted or granted, water rights by the DGA. In other words, the flow data of the water rights included in this database is less trustworthy. In order to determine which of those water rights were actually constituted, a thorough revision of the water rights expedients in the CIRH database was conducted.

833 water rights were found for the study area. 101 were eliminated for not being constituted in liters per second, and another 88 because it was proven through the revision of their expedient, that their constitution was denegated. As a result, 644 water rights records were utilized for the analysis.

It was detected that records of some expedients from the CIRH database do not exist. Due to this, two scenarios were generated with different flow distributions. The objective of this is to evaluate how the inaccuracy of a database can affect the water availability.

Upon obtaining the totality of the flows of the area, the sub-basin sum was computed, permitting the calculation of the water demand for each scenario.

Water balance

The water balance of the evaluated flows was conducted according to the norm established by the DGA. The permanent available flow corresponds to the PE flow of 85% minus the ecological flow, minus the already constituted permanent water right according to the following equation:

The ecological flow is considered as 50% of the flow with 95% exceedance probability, with the restrictions that Decreet N°71 (^{Ministerio del Medio Ambiente, 2015}) indicates, which are as follows:

For the available flows of eventual use, according to Equation (3), the Q10Pe minus the Q85PE minus the flow of already constituted water rights of eventual use, minus the possible deficit of permanent water rights generated by the availability analysis were used (^{DGA, 2008}):

Precipitation correction

The bias between TRMM and the instrumental observations reached differences of up to 91.5%. Given that the spatial distribution for the stations is irregular, it was opted to utilize TRMM to produce precipitation maps. However, the comparison between the TRMM precipitation and the stations delivered a bias of 33.9%. To reduce this bias, a correction of the amounts of each cell of the TRMM that cover this area of the study was conducted.

A relation between the altitude of the station and the bias of precipitations present with respect to the TRMM, since as observed in Figure 3, the higher the altitude of the station, the more the bias. Due to this, a correction using a linear regression model was conducted. Including Las Trancas station in the model gave a low R², so it was opted to eliminate it from the calculation. The Las Trancas station is the highest in the study area, and it is situated in a narrow valley zone, where a large part of winter precipitation corresponds to snow, whereas the other stations are located under the snow line determined for basins of that region (^{Stehr & Aguayo, 2017}). Since TRMM only estimates liquid precipitation, it is very likely that the lack of correlation can be explained by this. In this way, a model that explains a variance of 84% was obtained.

Figure 3 Linear regression model. 

The following is the adjustment equation of Figure 3:

The bias of each pixel was obtained with the equation (4) considering the corresponding elevations. These values were added to the TRMM, reducing the average bias to 14.8%, less than half of the initial bias. On the other hand, it is worth noting that, even if bias increased in some lower altitude stations, at higher altitudes the decrease was remarkable. The distribution in precipitation is shown in Figure 4. The number corresponds to the station ID (Table 1).

Figure 4 TRMM precipitation and bias in the weather stations. 

From the corrected model, a calculation of the average precipitation for the sub-basins and the reference stations was obtained, shown in Table 3 along with the corresponding area of each one. Point G corresponds to the pluvial regime zone of the Ñuble River, which added to point C results in the complete area of the basin.

Water surplus

Using the basin transposition method, the flows of natural regime present in Table 4 were obtained. The points located over the Ñuble River are those that present a larger flow, highlighting the river mouth with values over 150 m³/s at 85PE.

Additionally, from the Qma of the stations, and using equation 1 (basin transposition), the Qma of the evaluated points were calculated (Table 5). A large difference between the Ñuble and the other rivers is observed; for example, the mouth of the Changaral River is only approximately 8% the flow of the Ñuble River.

Water demand

The distribution of flows between permanent and eventual water rights was different. On the one hand, permanent rights have a more homogeneous distribution during every month of the year. On the other hand, eventual rights did show larger variability, reaching differences of up to 134 m³/s (Table 6) between the winter and summer months, with the flow being much higher in winter.

Scenario 2 shows that the uncertainty of a database can generate differences in granted flows by up to 5.2 m³/s. This is the case for Point G, which has verified permanent flows that oscillate between 25 and 30 m³/s (scenario 1), while non-validated water rights are considered, flows are up to 34.7 m³/s.

Water balance

The conducted balance gave similar results in both scenarios, with a deficit existing between the months of October and May, meaning that in a dry year there is not enough flow to satisfy all water rights.

Table 7 presents the availability in the evaluated points. The over-allocated flows, in which the demand is higher than the water surplus, are presented as negative. In addition to this, the symbol (*) represents flows that went from being available in scenario 1 to being over-allocated in scenario 2.

Although there is not a large difference between scenario 1 and 2, in 2 some new locations show over-allocation, mainly in permanent rights. The most drastic change is in Point G, in the month of February, where in scenario 1 there is an availability of 1.3 m³/s and in scenario 2 a deficit of 3.9 m³/s is produced. This situation is also generated in the Cato an Chillan rivers (points D and E) during the months of March and April, where in scenario 1 there is a higher availability with more than 0.3 m³/s and in scenario 2, the resource looks to be depleted with a deficit of up to 0.7 m³/s

The main deficits for the case of permanent rights, only considering scenario 2, are observed in points C and G, between the months of January and May (see Table 7 and Figure 5), with maximums that surpass 7 m³/s.

Figure 5 Permanent flow availability for scenario 2. 

By considering the global availability of the Ñuble River Basin, Point G can be identified as the most critical, since it generates the potential depletion of its contributing area. This is indicated by the hatched area in Figure 6, in which it can be observed that from February until May, the basin is over-allocated, meaning that in this basin no more rights can be granted, unlike the points located downstream (D, E, F and G) in which there exist availability.

Figure 6 Eventual flow availability for scenario 2. 

Figure 6 presents a similar situation, but it encompasses more months, where the Ñuble River Basin is seen low from November to April, not considering the Month of January, and the area of Point C shows the same situation in the months of January and October.

The main deficits for the case of eventual rights in scenario 2 occur in Points B and C, between the months of October and April, with maximums over 60 m³/s, and in the month of November (see Table 7 and Figure 6). On the other hand, points D, E and F show availability of the water resource throughout the entire year, but even then, in certain months, no Water Rights can be allocated due to the water deficit downstream.

Thus, the results indicate that an over-allocation of the resource exists in the summer months in scenario 1, that included every possible type of water right, and in scenario 2, when only the validated (DGA and CIRH) rights are considered.