# Hydrological Signatures Based on Event Runoff Coefficients in Rural Catchments of the Iberian Peninsula

ABSTRACT: Hydrological signatures are indices that help to describe the behavior of catchments. These indices can also be used to transfer information from gauged to ungauged catchments. In this study, different approaches were evaluated to determine volumetric runoff coefficients in 18 small/medium experimental gauged catchments of the Iberian Peninsula and to fit runoff calculations based on precipitation data for gauged and ungauged catchments. Using data derived from 1962 events, rainfall-runoff relationships were characterized and compared in order to evaluate the various hydrological response patterns. Volumetric runoff coefficients and cumulative runoff and precipitation ratios of the events that generated runoff (*R*_{cum}*)* minimized the root mean square error. A linear fit for the estimation of *R*_{cum} in ungauged catchments was based on mean annual precipitation, rates of infiltration, the fraction of forest-land use, and the catchment channel length. Despite high catchment heterogeneity, *R*_{cum} resulted in a suitable parameter to evaluate hydrological variability in rural gauged and ungauged catchments. In 50% of the catchments, the precipitation accounted for less than 50% of the runoff variation. Annual precipitation, antecedent rainfall, and base flow did not have a high significance in rainfall-runoff relationships, which illustrates the heterogeneity of hydrological responses. Our results highlight the need for signature characterizations of small/medium rural catchments because they are the sources of runoff and sediment discharge into rivers, and it is more economical and efficient to take action to mitigate runoff in rural locations.

** Guest Editor: Emmanouil Varouchakis**.

^{1}Agronomy and Forestry Engineering School, University of Córdoba, Cordoba, Spain.

^{2}Departamento de Geografía, Instituto Universitario de Ciencias Ambientales, Universidad de Zaragoza, Zaragoza, Spain.

^{3}Departamento de Proyectos e Ingeniería Rural, Campus de Arrosadia, Universidad Pública de Navarra, Pamplona, Spain.

^{4}Laboratorio Nacional de Genómica para la Biodiversidad, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Irapuato, Mexico.

^{5}Department of Agroforestry Engineering, University of Santiago de Compostela, Lugo, Spain.

^{6}Escola Superior Agrária–Instituto Politécnico de Castelo Branco, Castelo Branco, Portugal.

^{7}Centro de Estudos de Recursos Naturais, Ambiente e Sociedade, Escola Superior Agrária de Coimbra, Coimbra, Portugal.

^{8}Instituto de Agricultura Sostenible—CSIC, Córdoba, Spain.

^{9}DCH, Physical Geography, University of La Rioja, Logroño, Spain.

^{10}Center for Applied Geosciences, Faculty of Science, Eberhard Karls Universität Tübingen, Tübingen, Germany.

^{11}Facultad de Ciencias and Centro de Investigaciones Científicas Avanzadas (CICA), University of A Coruña, Campus de A Coruña, Coruña, Spain.

^{12}Geo-Environmental Research Group, Universidad de Extremadura, Cáceres, Spain.

^{13}Instituto Pirenaico de Ecología—CSIC, Zaragoza, Spain.

^{14}Hydro-Environmental Research Group, Science and Technology Faculty, University of the Basque Country, Leioa, Basque Country, Spain.

Address for correspondence: Dr. Encarnación V. Taguas, Agronomy and Forestry Engineering School, University of Campus Rabanales, Leonardo Da Vinci Building, Block 2, 1st Floor, CP 14014, Córdoba, Cordoba, Spain. E-mail: vtaguas@uco.es

Financial Disclosures/Conflicts of Interest: This research was supported by the research projects CGL2015-64284-C2-2-R, CGL2015-64284-C2-1-R, CGL2014-52135-C3-3-R, CGL2015-65569-R, CGL2014-56907-R, and AGL2015-65036-C3-1 funded by the MINECO-FEDER (Spanish Ministry of Economy and Competitiveness). E.N.-R. is the beneficiary of a Ramón y Cajal postdoctoral contract (Spanish Ministry of Economy and Competitiveness). For the remaining authors, none were declared.

Received April 29, 2017.

Accepted for publication July 17, 2017.

This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License 4.0 (CCBY-NC-ND), where it is permissible to download and share the work provided it is properly cited. The work cannot be changed in any way or used commercially without permission from the journal.

Understanding hydrological responses to rainfall events at the catchment scale is essential for developing policies that address water resources conservation and to evaluate the risks linked to a changing environment, changes in land use, urban development, and engineering infrastructure (^{Chow et al., 1988}; ^{Knapp et al., 1991}; ^{Mishra and Singh, 2003}; ^{Colin et al., 2011}; ^{Xing et al., 2015}). Hydrological spatiotemporal variability can be characterized by one or more indices, such as statistical parameters of runoff or catchment features and soft data, which define the catchment's hydrological signature (^{Hrachowitz et al., 2013}; Westerberg and McMillan, 2013; ^{Westerberg et al., 2016}). Signatures are crucial for characterizing the similarity of flow regimes between catchments and for out-scaling information from monitored ones (^{Alcázar and Palau, 2010}; ^{Belmar et al., 2011}).

Classic methods in hydrology, such as the rational method (^{Chow et al., 1988}) or the Soil Conservation Service Curve Number (1956), have parameterized basic rainfall-runoff relations through different interpretations of the term “runoff coefficient” (*R*_{c}). In general, *R*_{c} is associated with either (i) the ratio of the peak runoff rate to the rainfall intensity during the concentration time in the catchment or (ii) the ratio of the total runoff to the total rainfall (^{Dhakal et al., 2012}), with the latter being the simplest integrator-indicator of the catchment's hydrological behavior (^{Colin et al., 2011}; ^{Xing et al., 2015}). The statistical distributions of *R*_{c} and information derived from their percentiles (mean, median, 10th percentile, 90th percentile) are useful in interpreting variability of hydrological responses (^{Mishra and Singh, 2003}). However, these interpretations and their applicability may differ depending on the temporal scale used. Longer timescales, such as monthly, seasonally, or annually, are generally used to design storage infrastructure such as dams (^{Knapp et al., 1991}, ^{Taguas et al., 2015a}), whereas shorter timescales (event, subdaily, daily) are usually applied when analyzing floods, sediment load patterns, or geomorphologic/land use variations (^{Heiser et al., 2015}; ^{Duvert et al., 2012}; ^{Mateo Lázaro et al., 2016}). Estimation of runoff during individual storm events is not common, and so limited data availability (^{Belmar et al., 2011}) creates an important hydrological research gap in our understanding of the main driving factors of *R*_{c} (^{Dhakal et al., 2012}; ^{Li et al., 2015}; ^{Bennett et al. 2016}).

In the Iberian Peninsula (IP), human activities such as agriculture and urbanization can increase runoff coefficients and/or water demands, leading to a rise in the frequency and impact of periodic floods and droughts. Consequently, land-use changes may create higher vulnerability in the management of water resources (^{Belmar et al., 2011}). Numerous studies describe the possible alterations of runoff regimes (e.g., see ^{Batalla et al., 2004}; ^{Magdaleno and Fernández, 2011}; ^{Belmar et al., 2013}; ^{Wang et al., 2017}). However, comparative analyses at the event scale and in medium and small catchments are less common, despite the fact that these catchments are usually located in the headwaters of larger catchments. Small and medium catchments are also sites for implementing simple and inexpensive water conservation measures (^{Lana-Renault et al., 2011, 2014}; ^{Nadal-Romero et al., 2016}). The aim of this work was to evaluate hydrological signatures of IP rural experimental catchments at the event scale based on rainfall-runoff relationships and volumetric runoff coefficients. Event-scale rainfall-runoff datasets from 18 rural small/medium catchments were studied. The specific objectives were to (i) explore different signatures to determine representative volumetric runoff coefficients at the event scale and (ii) describe hydrological patterns of the catchments through their physical features (topography, soil, and land use), runoff coefficients, and rainfall-runoff relationships.

## MATERIALS AND METHODS

### Study Sites and Data Series

The IP is located in southwestern Europe. The peninsula has a surface area of 583,832 km^{2}, and its geographical limits include mainland Spain and Portugal, Andorra, Gibraltar, and the southernmost edge of France. The highest elevation is the Mulhacén peak, at 3,482 m above sea level. The IP environmental contrasts are the consequence of Atlantic Ocean westerly winds, the warming influence of easterly winds from the Mediterranean Sea, and the distribution of the main mountain ranges, oriented east-west, which divide the peninsula into three distinct large climatic areas: (i) the north coast; (ii) the midwestern and mideastern regions, reaching down to the south coast; and (iii) the Mediterranean coast (^{Peña et al., 2016}; Fig. 1A). The large midwestern region is subdivided into the North and South Plateau with elevations of more than 400 m above sea level. The topography strongly influences the distribution of climatic variables such as rainfall, temperature, and temperature gradients. Mean annual rainfall ranges from less than 300 mm in the southeast area (Mediterranean coast) to more than 1,200 mm, and up to 2,000 mm, in the west and north of the peninsula (Fig. 1B). The geology of the IP is the product of a long geological history from Proterozoic times to the present, which produced the complexity of its soils that were generated from igneous, metamorphic, and sedimentary rocks (^{MAGRAMA, 2016}).

Rainfall and runoff events recorded from 1996 to 2014 in 18 small rural experimental catchments (n = 1962) were analyzed to evaluate their runoff coefficients and rainfall-runoff relationships (Fig. 1; Tables 1 and 2). Table 1 describes the following attributes of the catchments: drainage area (*A*_{d}; ha); average annual rainfall (*P*; mm); average elevation from the digital elevation models of the catchments (*H*; m); channel length (*L*; m); channel slope (Sl; m · m^{−1}); soil type; dominant textural class; infiltration rate identified from categories A, B, C, and D of the Curve Number method (^{Soil Conservation Service, 1956}; Inf_Vel; cm · h^{−1}); and the surface percentage of land uses, considering agricultural crop fraction (ACF; %), agricultural orchard fraction (AOF; %), forest areas fraction (FF; %), rangeland fraction (RF; %), urban areas fraction (UF; %), and pastures fraction (PF; %). Drainage areas of the study catchments ranged from 1.4 to 1,600 ha, and the mean annual rainfall varied between 400 and 1,994 mm. Main land uses were agricultural crops, orchards, forest areas, and rangelands located at mean altitudes between 106 and 1,130 m above sea level.

Study periods and sample sizes in each catchment are presented in Table 2, with a mean of 109 ± 90 events. In order to standardize the analysis, the existence of base flow and the criteria considered for the event definition were checked. Only six catchments did not present base flow (Table 2), all of which, with the exception of Barranca de los Pinos (c_1), were located in the midsouthern area. In the other catchments, the base flow separation method of ^{Eckhardt (2005)} was applied to quantify direct runoff of each hydrograph. The definition of event was established in each catchment according to size (*A*_{d} and travel time), the hydrological response patterns, and the main objectives of the studies. Identification of events (Table 2) was based on runoff generation and intervals without rainfall pulses of 1 h (three catchments), 2 h (three catchments), 6 h (seven catchments), and 10 h (two catchments) and empirical evaluations of hyetographs and hydrographs (three catchments).

### Exploration of Representative Volumetric Runoff Coefficients at the Event Scale

#### Analysis of volumetric runoff coefficients at the event scale obtained from different methods

The cumulative runoff to rainfall ratios (*R*_{c}) and statistics (mean, median, range, 10th percentile, 90th percentile, SD) for each study catchment event were calculated in order to evaluate their basic attributes (Table 3). In addition to the classic definition of *R*_{c}, runoff coefficients following Hawkins' graphical method (*R*_{c}*_*H; ^{Dhakal et al., 2012}), Curve Numbers (CN) obtained from Table 9-1 in ^{USDA-NRCS (1997)} for the characteristics of the study catchments (soil, type of vegetation cover, land use/treatment, hydrological condition), the “mean” soil moisture state (antecedent moisture condition II), and the cumulative runoff to rainfall of the events (*R*_{cum}) were considered to explore the most suitable approach for calculating runoff through rainfall values. *R*_{c}*_*H is obtained from the asymptotic exponential relationship between runoff coefficients of each event (*R*_{c}) and their corresponding rainfall values. This value represents the runoff coefficient for high rainfall events producing high soil moisture. The example in Fig. 2 shows a typical scatter plot for Aixola (c_3) and an exponential fit with asymptote. In the case of Curve Numbers of the USDA-NRCS methodology, the runoff (*Q*; mm) is calculated with Eq. 1 through 4:

where *S* is the potential maximum retention (mm), defined by the dimensionless parameter CN (Eq. 2); *I*_{a} is the initial abstraction (mm) consisting mainly of interception, infiltration, and surface depression storage during early parts of the storm, and *P* is the event rainfall (mm).

The performance of different runoff coefficient indices to calculate event runoff through rainfall was checked. The root mean square errors (RMSE) of the observed and estimated runoff when the indices were multiplied by the rainfall of each event were compared, as well as their correlation coefficients (*r*). These analyses were only applied on the catchments with a data series of n > 10 events; catchments 2 and 8 were therefore discarded.

#### Prediction of representative runoff coefficients through multiple linear regression

After evaluating the most suitable index for gauged catchments, a multiple linear regression (MLR) was employed to relate the main physical features of the catchments (Table 1) with the representative value of runoff coefficient. This was done in order to find a fit that could be used in ungauged catchments. The coefficients for the significant variables and *P*-level of significance were calculated, and the final fit was tested through the *F* test, the RMSE of the observed and predicted values, and the coefficients of determination *R*^{2} and adjusted *R*^{2} (adj. *R*^{2}, which considers the number of degrees of freedom in the analysis). These calculations were carried out using Statistica 8 software (^{Stat Soft Inc., 2008}).

### Hydrological Patterns and Environmental Features in the Study Catchments

Event rainfall-runoff scatterplots were evaluated for each catchment, as well as the regression coefficients and *R*^{2} of their corresponding fits. The different types of fits were classified according to observed trends of the calculated regression coefficients (parameters *a* and *b*) and of *R*^{2} (group of catchments where the rainfall event accounts for >50% of the runoff variance, 0.50 < *R*^{2}, and catchments where the rainfall event accounts for <50% of the runoff variance, 0.50 > *R*^{2}). In addition, the effects of the antecedent soil moisture on the runoff response were studied through analysis of the accumulated previous rainfall (APR) on the rainfall-runoff relationships. Consequently, APR was added as a factor to the MLR (*Q = a* * *P + b* * APR *+ c*) to evaluate previous rainfall contribution to the *R*^{2} and its significance. With the exception of five catchments (c_4, c_5_c_6, c_14, and c_17), where the previous rainfall period was 7, 15, and/or 21 days, the number of days prior to the event was 10. When different intervals of APR were available, the fit was tested with each of them.

Finally, a principal component analysis (PCA) was used in order to explore the influence of the physical attributes of the catchments on the type of linear fit and the influence of base flow. The aim of this methodology was to isolate the catchments by means of common linearly grouped attributes (^{Malinowski, 1991}). In PCA, the initial variable matrix is changed to noncorrelated synthetic variables called *principal components* in order to concentrate the analysis on the variables that contribute to the most variance. On the principal axes, the catchment coordinates are the result of contributions of the variance of each studied variable (feature) to the axis. A main axis represents more or less information about a variable according to the value of the principal component, which is equivalent to its degree of correlation. A set of 16 catchments with 12 variables/attributes {*X*_{i}(*w*_{j})*}*: *A*_{d} (ha), *P* (mm), *H* (m), Sl (m · m^{−1}), Inf_Vel (cm · h^{−1}), ACF (%), AOF(%), FF(%), RF (%), UF (%), PF(%), and *R*_{cum}, were considered. The following steps were taken: (1) the correlation matrix between variables was calculated; (2) the correlations matrix diagonal was set up, and the eigenvalues and eigenvectors for the space change obtained; (3) the projections of individual cases (catchments) on the new axis were calculated; (4) the projection of the variables on the main plane was also calculated to determine their contribution to the formation of each axis; (5) the quality of the representation of the variables and individuals was tested (distances of the projections to plane) to verify the quality of the representation in the principal plane These steps were carried out using Statistica 8 software (^{Stat Soft Inc., 2008}).

## RESULTS AND DISCUSSION

### Representative Volumetric Runoff Coefficients at the Event Scale

#### Basic statistics and preliminary analysis

Table 3 presents the mean, median, minimum, maximum, SD, and 10th and 90th percentiles of *R*_{c} in the catchments. Catchments c_2 and c_8 were considered unsuitable for calculating the global statistics because they each had less than 10 events. The mean *R*_{c} varied between 0.03 (Corbeira, c_16) and 0.42 (Landro1, c_7) with an average of 0.14 ± 0.13. Landro1 (c_7) is the catchment with the highest annual rainfall (nearly 2,000 mm). Although it contains other land uses, rangelands dominate c_7, whereas Aixola (c_3) is a forest catchment with steeper slopes and a mean annual rainfall of 1,440 mm (Table 1). Corbeira (c_16) and Casal das Hortas (c_18) also showed values less than 0.14 (0.03 and 0.07, respectively). Both catchments were characterized by smoother topography, and the fraction of forested area was close to 70%. However, they are quite distinct in terms of *A*_{d} size (1,600 and 150 ha, respectively) and soil types (Umbrisol-Cambisol and Regosol-Fluvisols, respectively). Analysis of the medians show only five catchments (c_2 was excluded) with a central value of their distribution larger than 0.10, which illustrates that under dry conditions most expected runoff coefficients are less than 10%. In 11 of the catchments, the 90th percentiles of *R*_{c} were greater than 0.30, with a maximum of 0.64 in Landro1 (c_7) and a minimum of 0.06 in Corbeira (c_16), which is the largest catchment.

^{Norbiato et al. (2009)}, found a similar range of volumetric runoff coefficients (between 0.04 and 0.48) and an SD (0.13) close to that of the present study in 14 forest and rangeland catchments in the Italian Alps. However, it was significant how the *R*_{c} mean of the catchments was notably greater (0.28) than in this study (0.14). ^{Dhakal et al. (2012)} observed wider variation intervals for a group of 90 developed and undeveloped catchments in Texas. In fact, *R*_{c} means of these catchments varied between 0.10 and 0.67, whereas the *R*_{c} medians ranged between 0.06 and 0.76. The influence of developed areas may explain, among other environmental aspects, the notable differences highlighted by the authors to explain *R*_{c} variance.

#### Comparison of indices for gauged catchments

Table 4 presents a summary of the analysis used to compare RMSE values of runoff obtained when different runoff coefficient indices are considered. The numeric values of the runoff coefficients considered and the RMSE derived from the observed and calculated runoff are shown in Table 4. In addition, the correlation coefficients between observed and calculated runoff and their significance are presented in the columns marked (1) and (2). For *R*_{c}*_*H, *R*_{c}*_*med, *R*_{cum}, and *R*_{c}*_*mean, very close values of *r* were obtained, and they are presented in column (1), whereas column (2) indicates *r* values for the analysis with CN.

For all the catchments, the most suitable indices that minimized RMSE were *R*_{c}*_*H and *R*_{cum} (Table 4), with the exception of Landro1 (c_7), where CN was the parameter that optimized the error. Evidently, the CN are not derived from the data series, and these results could be expected (^{Hjemfelt (1991)}. Only *R*_{c}*_*H presented clearly better results than *R*_{cum} in Aixola (c_3), whereas in the other catchments both values were very close, or *R*_{cum} provided the best performance. Both indices were strongly correlated (*r* = 0.93, *P* < 0.05; Fig. 3); however, *R*_{cum} has the clear advantage of being calculated directly from the data series without graphical analysis. In fact, it is worth noting that the *R*_{cum} index provided a good performance for a heterogeneous group of catchments, and it is easy to calculate in gauged catchments.

The coefficients of correlation calculated for the best fits were greater than 0.60 in all catchments with the exception of Parapuños (c_15; *r* = 0.55; Table 4). Note that *R*_{c}*_*median, usually considered as a reference statistic to select the representative CN of a site (^{Soil Conservation Service, 1956}), showed a weak correlation (*r* = 0.17) with the CN values. *R*_{c}*_*median provided minimum or close to the minimum RMSE for Arnás (c_12) and Casal das Hortas (c_18) only, whereas CN and *R*_{c}*_*mean presented the maximum RMSE (Table 4). The range of CN (Table 4) presented an average of 73 and a variation range between 54 and 84. The worldwide success of the CN methodology in calculating storm runoff is that it is well supported by empirical data (^{Mishra and Singh, 2003}). However, after checking its suitability in olive orchard catchments in Spain, ^{Taguas et al. (2015b)} suggested reevaluating its application with empirical data. ^{Dhakal et al. (2012)} compared the indices of volumetric runoff coefficients obtained from different approaches for catchments in Texas and underlined the lack of correlation among them, which supports the need for studies to check the information in design manuals with badly justified hydrological parameterizations.

#### Prediction of runoff coefficients for ungauged catchments

Table 5 shows the results of the prediction of *R*_{cum} with multilinear regression with the best combination of catchment attributes (Table 1). The model (*R*_{cum} *= b*_{0} *+ b*_{1} * *P + b*_{2} * Inf_Vel *+ b*_{3} * FF *+ b*_{4} * *L*) depended on *P* (mm), Inf_Vel (cm), FF (%), and *L* (m), which illustrates the expected influence of climate, soil type, land cover, and size of catchment. Dependence on similar catchment features were described by ^{Norbiato et al. (2009)} for event runoff coefficients observed in 14 catchments in the eastern Italian Alps. Despite catchment heterogeneity, the values of significance for the *F* test (0.0006) and adj. *R*^{2} (0.73) indicate that most of the variance was satisfactorily explained by the model. The RMSE was 0.05. Significance of the coefficients was less than 0.10, with the exception of the intercept. Figure 4 presents the scatterplot of the observed and predicted *R*_{cum} values. It is worth noting how catchments Aixola (c_3) and Tejería (c_5) presented the maximum deviation, and their *R*_{cum} values were notably overestimated. In contrast, the values from San Salvador (c_14) were underestimated (Fig. 4).

The quality of the fittings is comparable with those in ^{D'Ambrosio et al. (2017)}, who calculated maximum annual flow in terms of significant variables in temporary river systems in Italy. Moreover, similar weaknesses were noted by ^{D'Ambrosio et al. (2017)} in relation to the reduced number of catchments and attributes analyzed, which must also be recognized in our study. However, we would like to highlight that (i) abundant literature exists showing daily, monthly, and annual stream flows (mainly quantiles and statistical moments) and their regionalization for large gauged and ungauged catchments (^{Sanborn and Bledsoe, 2006}; ^{Alcázar and Palau, 2010}; ^{Belmar et al., 2013}), but there is a notable gap at the event scale and for small catchments (^{Merz et al., 2006}; ^{Norbiato et al., 2009}), and (ii) for a small group of simple features of the catchments, representative runoff coefficients could easily be estimated. In order to improve the statistical performance, more effort should be made to contrast the results by adding new catchments in different climatological areas of the IP, as well as by enlarging the data series.

### Hydrological Patterns and Environmental Features

Table 6 and Figs. 5 and 6 show the results of the classification analysis to evaluate hydrological patterns in the study catchments. Derived from the evaluation of *R*^{2} on the *P-Q* fits, in 50% of the catchments, rainfall accounted for less than 50% of the runoff variation. Figures 5A of Parapuños (c_15) and 5b of Landro 1 (c_7) show representative rainfall-runoff scatterplots, which present the different trends. The range of variation of *R*^{2} was between 0.30 (Parapuños, c_15) and 0.94 (Landro1, c_7). The term “*a*” (Table 6) varied between 0.07 (Casal das Hortas, c_18) and 0.65 (Landro1, c_7), whereas “*b*” did so between −12.78 (Landro1, c_7) and −0.02 (Casal das Hortas, c_18). Although *R*_{cum} was slightly less than the term “*a*” (approximately 30%), both indices were very well correlated with *R*_{cum} (*r* = 0.95, *P* = 0.000). For 50% of the catchments, “*a*” was between 0.20 and 0.30, and this is where the best fits were concentrated, with the exception of Landro1 (c_7) and La Conchuela (c_9).

As far as the effects of antecedent precipitation are concerned, APR did not improve the coefficients of determination of the fits when this factor was included in the MLR model (Table 6). Only in Casal das Hortas (c_18) was the increase in adj. *R*^{2} substantial (from 0.38 to 0.51). In addition, APR presented a significance *P* > 0.05 in six catchments (38%; Table 6): Aixola (c_3), Latxaga (c_4), Araguás1 (c_6), Puente Genil (c_11), San Salvador (c_14), and Corbeira (c_16). With the exception of Corbeira (c_16), the channel mean slopes of those catchments were larger than 7%, which may indicate steeper slopes and shallower soils and a reduced influence of these variables on runoff generation. It is worth noting that the patterns of runoff generation must be controlled by local physical factors (different from APR) whose spatial variability determines the response in the outlet. ^{Schnabel and Gómez-Gutiérrez (2013)} mentioned the importance of soil moisture in the valley bottoms as a key factor to understand the hydrological behavior of Parapuños (c_15). The different response patterns of the catchments such as Araguas1 (c_6) and Araguas2 (c_17) also illustrate the need for specific analysis of the catchments to describe their hydrological behaviour.

Table 7 and Fig. 6 summarize the result of the PCA. The eigenvalues and the percentage of explained variance for each principal axis were as follows: for axis 1, 2.70 and 22.48%; for axis 2, 2.25 and 18.73%; for axis 3, 1.82 and 15.16%; for axis 4, 1.57 and 13.04%; for axis 5, 1.31 and 10.89%; and for axis 6, 1.15 and 9.59%, whereas for the rest of the axes the explained variance was less than 5%. The fourth main axis was correlated with *R*_{cum} (projection on PA4 = −0.80) and *P* (PA4 = −0.75), and the variance explained by PA4 was not much lower than the variance explained by the second main axis. If the plane formed by the principal axes 1 and 4 is considered, the cumulative variance adds up to 36%. *P*, *H*, Inf_Vel, AOF, RF, and PF were acceptably represented on the first axis (projection on PA1 > 0.55; Table 7), whereas *P and R*_{cum} were on the fourth axis. This is shown in Fig. 6, where the influence of the sign of the projection on the distribution of the catchments (cases) on the principal plane is also indicated. In Fig. 6A, the great heterogeneity of the eight catchments with acceptable linear rainfall-runoff fits can be observed (*R*^{2} > 0.50). For example, five catchments (Araguás2, Barranca, Arnás, Landro1, and Aixola; c_17, c_1, c_12, c_7, c_3, respectively) were characterized by their land use other than agriculture, the highest value of the annual rainfall and mean altitude, and the high infiltration velocities associated with sandy and loamy textures. On the other hand, despite their agricultural land use and lower values of annual rainfall and altitude, La Parrilla, Setenil, and Conchuela also showed a strong sensitivity to the event rainfall (*R*^{2} > 0.50, Fig. 6A; Table 1). The other group of catchments was characterized by four agriculture and pasture land uses (Parapuños, Puente Genil, La Tejería, Latxaga; c_15, c_11, c_5, c_4, respectively), and another four were forest/rangeland catchments with a low variability (with the exception of Landro1, c_7) in terms of annual rainfall range and *R*_{cum}.

Figure 6B illustrates the lack of correlation between *R*_{cum} and the presence of base flow in the catchments. In other words, a higher *R*_{cum} (which can be found in the third and the fourth quadrants) did not mean a greater frequency of catchments with base flow. Finally, the influence of *A*_{d} was not significant to explain the variance, and it made a negligible contribution toward the formation of axes (Table 7). The event criteria shown in Table 2 did not explain any tendency of the catchments derived from Fig. 6. Finally, another point to underline, which was not included in PCA but can be described if the distribution of catchments is considered, is the low effect of geographical proximity in determining similar hydrological features. This fact can be particularly evident in Araguás1, Araguás2, and San Salvador (Figs. 1 and 6), and it might illustrate the complex hydrological response of the catchments. These findings contrast with analyses carried out in other more humid areas or in the IP. For instance, ^{Mathias et al. (2016)} described the nonlinearity of rainfall-runoff in catchments in the United Kingdom associated with more arid catchments in terms of base flow, low rainfall, and evaporative demand. ^{Belmar et al. (2011)}, referring to the analysis of 390 sections of the Segura River Basin in Spain, described four hydrological categories (large rivers, perennial stable streams, perennial seasonal streams, and intermittent and ephemeral streams) with a high spatial correlation in the response pattern of monthly and annual flow.

Although APR must have influenced the runoff generation, it has a low contribution to explain the runoff at the event and catchment scales. On the other hand, neither the annual rainfall nor the presence of base flow had a clear influence on rainfall-runoff relationships, probably as a result of very different environmental and experimental conditions in the aforementioned cases. Apparently, higher infiltration rates and less forested area may involve less memory or closer initial soil moisture conditions and therefore more constant (linear) response patterns to rainfall. There is a persistent demand for studies that use hydrological indices/signatures to establish criteria to group hydrological regimes in order to identify, among other factors, ecological aspects and the behavior of rivers (^{Baeza-Sanz and Garcia de Jalon, 2005}; ^{Poff et al., 2010}; ^{D'Ambrosio et al., 2017}). Despite the heterogeneity of the catchments, rainfall-runoff patterns at the event scale have allowed us to group the catchments into a small number of different response types. Management of small rural catchments is essential because their contribution to rivers in terms of sediment (and water quality) may lead to serious risk of floods, as well as damage to ecological systems. Thus, the characterization of flow patterns of small rural catchments (or signatures) in terms of magnitude and susceptibility of response can provide guidelines for planning and implementation of measures to deal with source areas of runoff and sediment, which are eventually discharged into large rivers.

## CONCLUSIONS

In a context of the lack of experimental measurement-based runoff coefficients of small rural catchments in the IP, our results illustrate an empirical method to determine the representative volumetric runoff coefficient for gauged and ungauged catchments. The event rainfall accounted for more than 50% of the event runoff variance in 50% of the catchments. The catchments were highly heterogeneous in terms of land use and location in the IP, and neither annual rainfall nor base flow presence contributed significantly to explaining the rainfall-runoff patterns. The previous rainfall had a variable and irrelevant influence on the runoff generation. A greater effort needs to be made to describe and analyze small/medium rural catchments because taking action at this scale can be more economical and efficient than planning measures that are focused solely on the riparian areas of large rivers.

## REFERENCES

**Keywords:**

Catchments; Iberian Peninsula; runoff; runoff coefficients