Assessment of hydrological and seasonal controls over the nitrate flushing from a forested watershed using a data mining technique

A data mining, regression tree algorithm M5 was used to review the understanding of mutual hydrological and seasonal settings which control the streamwater nitrate ﬂush-ing during hydrological events within a forested watershed in the southwestern part of Slovenia, characterized by distinctive ﬂushing, almost torrential hydrological regime. 5 The basis for the research presented an extensive dataset of continuous, high frequency measurements of seasonal meteorological conditions, watershed hydrological responses and streamwater nitrate concentrations. The dataset contained 16 recorded hydrographs occurring in di ﬀ erent seasonal and hydrological conditions. Based on pre-deﬁned regression tree pruning criteria, a comprehensible regression tree model was 10 obtained in the sense of the domain knowledge, which was able to adequately describe most of the streamwater nitrate concentration variations (RMSE = 1.02 mg/l-N; r = 0.91). The attributes which were found to be the most descriptive in the sense of streamwater nitrate concentrations were the antecedent precipitation index (API) and air temperatures in the preceding periods. The model was most successful in describ-15 ing streamwater concentrations in the range 1–4 mg/l-N, covering large proportion of the dataset. The model performance was poorer during the periods of high streamwa-ter nitrate concentration oscillations (up to 7 mg/l-N during the summer hydrographs and 14 mg/l-N during the extreme November hydrograph) related to highly variable hydrological conditions, which would require a less robust regression tree model. 20


Introduction
In recent years, the export of nitrogen from forested watersheds has become an important research area and a public policy issue since nitrogen leaching can strip nutrients from forest soils, acidify streams and cause eutrophication (Vitousek et al., 1997;Fenn et al., 1998;Lovett et al., 2002;Wade et al., 2002;Fitzhugh et al., 2003).The variability in nitrogen loss from forested watersheds is high and has been ascribed to many EGU causes, including differences in atmospheric nitrogen inputs (Stoddard, 1994;Aber et al., 2003), pedology (Gundersen et al., 1998), forest history (Goodale et al., 2000) and hydrology (Hornberger et al., 1994;Creed et al., 1996).
The hydrologically induced mobilization of nitrate as the most mobile form of nitrogen from the undisturbed, forested watersheds has received considerable attention in recent hydrological and biogeochemical studies (Creed et al., 1996;McHale et al., 2002;Beachtold et al., 2003;Weiler and McDonnell, 2006).Nitrate concentrations in the streamwater draining forested watershed provide the fundamental information about biogeochemical processing of nitrogen in the forest ecosystem (Burns, 1998;Goodale et al., 2002).At seasonal boundaries, accumulation of labile dissolved inorganic nitrogen in excess of physical and biological retention capacity tends to occur (Likens and Boremann, 1995;Cirmo and McDonnell, 1997;Lovett et al., 2002;Vanderbilt et al., 2003).Both autumn and spring streamwater nitrate pulses are usually observed, with autumn increases in the nitrate concentration associated with a greater amount of precipitation and diminished biological assimilation, whereas spring pulses are reported mainly from watersheds with snowmelt driven hydrology (Arheimer et al., 1996;McHale et al., 2000;Langusch and Matzner, 2002;Sickman et al., 2003;Clark et al., 2004).
The understanding of how hydrological conditions trigger flushing of labile nutrients on a watershed scale is still rather poor, especially when we move from the timescale of seasonal variability towards the timescale of a single hydrological event.The main differences in the explanation of the hydrologically driven export of nitrate found in the literature are not necessarily contradictory as they can be ascribed to discrepancies in basic hydrological and climatological conditions, topography, forest soil characteristics and biogeochemical behavior of forest ecosystems (Cirmo and McDonnell, 1997;Andersson and Lepisto, 1998;Aber et al., 2002;Worall et al., 2003;Stieglitz et al., 2003;Binkley et al., 2004).
The inability to obtain an insight into the interactions between the hydrological and biogeochemical states, which control the nitrate flushing mechanisms, lies in the com-Introduction

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EGU plexity of event-scale hydro-biogeochemical observations.Studies of the hydrologically induced nitrate export behaviour from forests are observed mainly at low time frequencies, which do not allow tracing the behavior of nitrate export during a particular hydrological event.In order to understand how hydrological flowpaths affect stream chemistry and, conversely, to use stream chemistry to decipher hydrological processes, we need chemical measurements at time scales that correspond to the hydrological dynamics of an observed hydrologic unit (Kirchner et al., 2004).
Our study presents an investigation of interacting seasonal and hydrological conditions which strongly influence the export of nitrate from a forested watershed in the SW part of Slovenia.The continuous high-frequency measurements of streamwater nitrate concentration in the periods of hydrological events in different seasons provided the ability to study the nitrate export behaviour predefined by seasonal meteorological settings and conditioned by the hydrological events observed.The results of the measurements show that seasonal biogeochemical settings play an important role in controlling the size of the forest soil nitrate pool which is available for further mobilization through hydrological mechanisms.
The continuous tracing of nitrate concentration in streamwater requires substantial effort and resources.Based on our continuous observations of nitrate export during more than 15 recorded floodwaves, a considerable amount of data was acquired.This paper aims at presenting the application of data mining (DM) and knowledge discovery from database (KDD) tool, namely regression or model trees, for gaining new knowledge about the observed behaviour of seasonally and hydrologically influenced mobilization of nitrate during hydrological events and applying this knowledge to better understand the streamwater nitrate concentration behaviour.

Study area
The Padež stream watershed is situated in the southwestern part of Slovenia and comprises 42.1 km 2 (Fig. 1).The Padež stream is a tributary of the Reka river, one of the

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The Padež stream watershed is minimally disturbed by human activity; it has already been used for drinking water supply and, as such, it is also foreseen as an additional source of drinking water for the water-deficient area of the Slovenian coastal region.According to the CORINE 2000 land cover data, 82% of the watershed is covered by forest (79% by broad-leaved forest), and 18% of the watershed comprises complex cultivation patterns (mainly meadows with significant areas of natural vegetation) which are all in the state of successive afforestation.Lower parts of the watershed are almost completely covered by deciduous forest.Main tree species that can be found in the Padež watershed are Sessile oak (Quercus petraea), Black alder (Alnus glutinosa), Beech (Fagus sylvatica L.), and Hornbeam (Carpinus betulus) (Slovenian Forest Service, 2000).

Monitoring system
The monitoring system at the Padež watershed is shown in Fig. 1.Precipitation data were obtained from tipping bucket rain gauges located within the Padež watershed; the meteorological data were gathered from the automatic meteorological station positioned in the middle of the watershed (Fig. 1).Water level was recorded continuously with a 5-min time step on four locations using a 1-D Doppler instrument with an integrated logger.Flow was gauged on stream sections equipped with limnigraphs using two instruments.During low flow conditions, a salt-dilution flowmeter was used, whereas during middle to high flows, a 2-D/3-D handheld Doppler velocimeter was used.The resulting water-level records were converted to volumetric discharges by empirical ratings that were validated by gauging at different flow levels.
Stream chemistry was measured continuously on a 30-min time step using a water quality multi-parameter data-sonde.The multi-parameter sonde is designed for on-site and flow-through applications and measures water chemistry parameters simultane-Introduction

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EGU ously (Brilly et al., 2006).The multiple parameters include: nitrate, temperature, electric conductivity, depth, dissolved oxygen, Total Dissolved Solids (TDS), Oxidation Reduction Potential (ORP) and pH.Additionally, grab water samples were taken biweekly from January to November 2006 at the site where the multi-parameter sonde was installed for laboratory analysis in order to control the multi-parameter sonde readings.
The samples were collected and preserved according to SIST EN ISO 5667-6 and SIST EN ISO 5667-3 standards, respectively.Nitrate was measured according to SIST EN ISO 10304-1 standard with the ion chromatograph.A comprehensive description of the monitoring system settings is given by Rusjan et al. ( 2007)1 .

Regression trees
Regression trees as a subgroup of decision trees are a representation for piece-wise constant or piece-wise linear functions.Like classical regression equations, they predict the value of a dependent variable (called class) from the values of a set of independent variables (called attributes) (Džeroski, 2001;Witten and Frank, 2005).Regression trees are an especially attractive type of models for three main reasons.Firstly, they have an intuitive representation, the resulting model is easy to understand and assimilated by humans (Breiman et al., 1984).Secondly, the regression trees are nonparametric models, no intervention being required from the user, and thus they are very suited for data mining (DM) and knowledge discovery from database (KDD) (Džeroski, 2001;Atanasova and Kompare, 2002).Lastly, the accuracy of decision trees is comparable or superior to other models (Witten and Frank, 2005).Compared to neural networks, a more commonly used machine learning method in hydrological studies, regression trees can give a structural insight into the hydrological processes being modeled ( Štravs and Brilly, 2007).Introduction

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The regression tree construction proceeds recursively, starting with the entire set of training examples.At each step, the most discriminating attribute is selected as the root of the (sub)tree and the current training set is split into subsets according to the values of the selected attribute.The split variable selection is one of the main components of classification tree construction.The quality of the split selection criterion in tree nodes has a major impact on the quality (generalization, interpretability and accuracy) of the resulting tree.For regression trees, the selected split is the one that maximizes the homogeneity of the two resulting groups with respect to the response variable (Prasad et al., 2006).In order to avoid the overfitting of the regression trees to the training data, many techniques, called pruning, have been proposed in the literature (Witten and Frank, 2005).
In our study of the nitrate flushing, a re-implementation of the well known regression tree induction algorithm M5 (Quinlan, 1992) within the software package WEKA (Wang and Witten, 1997;Witten and Frank, 2005) was used.Each leaf of the generated regression tree contains a linear regression equation which is used to model the dependant class inside the subset of instances classified to the particular leaf.The prediction accuracy of the constructed models was evaluated performing 10-fold crossvalidation (Kohavi, 1995).In the 10-fold cross-validation, the dataset is randomly split into 10 disjoint subsets of approximately the same size, and 10 experiments are performed.In each of these, 1 of the 10 subsets is withheld, the prediction method trained on the union of the remaining 9, then tested on the unseen examples from the withheld subset.The reported accuracies are the averages of the 10 experiments.
The attribute selection considered in the data mining applications should be based on the domain knowledge of the modeled processes (Hall et al., 2002;Zaffron, 2005).The attributes which were considered in the dataset used for the construction of regression tree models of the streamwater nitrate concentration are listed in EGU a certain time step represents an instance used in the data mining process.Within a particular region or forest stand, mineralization and nitrification rates vary considerably in response to two key factors: temperature and moisture (Arheimer et al., 1996;Andersson and Lepisto, 1998;Bernhardt et al., 2002;Vanderbilt et al., 2003).Furthermore, Clark et al. (2004) used mean monthly air temperature to describe the mean monthly streamwater nitrate concentrations in forested watersheds, however, without a detailed consideration of the possible effect of changed hydrological conditions.With particular attribute selection we therefore tried to capture the possible hydrological and seasonal characteristics which most likely play an important role in regulating streamwater nitrate responses during the observed hydrological events.In order to describe the preceding watershed wetness state we used the antecedent precipitation index (API x ) for a selected period of x preceding days using the method of Linsley et al. (1982), whereas the characteristics of the hydrological events are captured through the sums of rainfall (Psum) for 3, 6, 12, 24 and 48 preceding hours and the observed discharges of the Padež stream.Additionally, the characteristics of the rainfall runoff formation are considered within the data about the proportion of event water in the total discharge (EW).The proportion of event water in the total discharge was obtained performing the two-component hydrograph separation using electrical conductivity of rainfall and streamwater as a natural tracer (Rusjan et al., 2007  1 ).On the other hand, possible seasonal implications in the sense of temperatures are considered through the data about average hourly air temperatures for the periods of 1, 3, 7 and 14 preceding days and the streamwater temperatures.

Results and discussion
In order to obtain an overview of the great complexity of seasonally and hydrologically induced streamwater nitrate concentrations and to make the resulting regression tree models more comprehensive, Fig. 2 shows the recorded hydrological events in different seasons and associated streamwater nitrate oscillations which were included into Introduction

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the data mining process.The streamwater nitrate concentrations during the baseflow conditions were generally in the range of 1-1.5 mg/l-N.During the first two recorded hydrographs in early spring (March and April hydrographs), the streamwater nitrate concentrations showed no responsiveness to the changed hydrological conditions.The concentrations remained around 2 mg/l-N.On the other hand, the hydrological events in late spring and summer during the sequences of May, June and especially August expressed the strong influence of changed hydrological state on the streamwater nitrate concentration increases up to 7 mg/l-N.The greatest increase in the streamwater nitrate concentration was observed during the hydrological event in November, when streamwater nitrate concentrations exceeded 14 mg/l-N.

Regression tree model
The size of the generated trees which depends on the predefined number of instances that reach a tree leaf as a pruning factor is shown in Fig. 3.The resulting performances of the trees in predicting the streamwater nitrate concentration expressed through RMSE and correlation coefficient r are given in Fig. 4. The regression trees with a small number of instances in the leaves are extremely big; in the case of only five instances in a leaf, the generated regression tree has 73 rules -linear regression equations in leaves.The performance of the trees with a large number of rules is suspiciously high (in the case of the tree with 73 rules the RMSE=0.40mg/l-N and r=0.99).
However, a tree of such size is practically incomprehensive and very likely overfitted to the training data.In order to avoid the problem of overfitting and improve the comprehensiveness of the resulting regression trees we have opted for a more drastic pruning of the regression tree by increasing the number of the instances in the leaves.

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EGU two suitable regression trees are: in the case of a regression tree with 100 instances in leaves RMSE=0.97mg/l-N and r=0.92; in the case of 125 instance regression tree RMSE=1.02mg/l-N and r=0.91.The decrease in the performance of the two regression trees is relatively small whereas the size of the regression tree with 125 instances in leaves is additionally decreased (10 rules) vs. regression tree with 100 instances in the leaves (14 rules).We have therefore decided for the regression tree with 125 instances in the leaves.In Table 2, a list of linear regression equations -rules generated for the leaves of the resulting regression tree is given with a schematic representation of the regression tree.The splitting attribute selected in the root node of the resulting regression tree is the antecedent precipitation index for the period of 5 preceding days API 5 .According to the splitting value of the API 5 =17.9 mm the two resulting branches interpret the states of high hydrological wetness of the watershed (values above 17.9 mm), whereas the branch defined by values of API 5 below 17.9 mm is used to describe the hydrologically less moist periods.On the second split level, avgT 3 (value 10.1 • C) and avgT 14 (value 11.6 • C) were selected to describe the seasonal character of the hydrological events.
The result of the splitting on the first two split levels is four branches of the regression tree (Table 2).The split of the dataset into four branches according to the conditions imposed on the first two split levels of the regression tree is shown in Fig. 5. From the temporal point of view, branch 1 covers the data obtained during the hydrologically less moist, early spring period (March and April) and the short period before the occurrence of the November hydrograph.Branch 2 includes the data obtained during the rising limbs of the first hydrographs in the sequences of the late spring and summer hydrographs in May, June, August and September, whereas branch 4 covers the rest of the data obtained during the late spring and summer periods.Branch 3 comprehends the November hydrograph and part of the March hydrograph.
On the lower, third split level, we can find Psum 12 h and Psum 24 h , which characterize the properties of the hydrological events in more detail.On the fourth and fifth split levels avgT 14 , avgT 7 and API 14 are selected for further splitting.Interestingly, the resulting Introduction

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EGU regression tree model does not include the data about discharge Q and streamwater temperature TW as a split attribute nor as an attribute included into the linear models in the leaves.However, the discharge is considered indirectly through the EW attribute, which appears in the linear models Nos. 8 to 10 (Table 2).
The measured streamwater nitrate concentrations vs. streamwater nitrate concentrations predicted by the regression tree model are shown in Fig. 6.The regression tree model successfully predicts low to medium nitrate concentration (1 mg/l-N to 4 mg/l-N).
The accuracy of the model prediction decreases with an increase in the streamwater nitrate concentration.The regression tree model with 10 leaves seems to be too robust to be able to more accurately predict high streamwater nitrate concentrations (above 5 mg/l-N concentrations) which occur only during short periods of hydrograph peaks (Fig. 2).Furthermore, the model does not predict nitrate concentrations above 9 mg/l-N, while the measured concentrations during the November hydrograph peak discharges rose to 14 mg/l-N.

Interpretation of the model results in the light of domain knowledge
The structural transparency of the regression tree models offers additional opportunities to interpret not only the model results in the sense of performance but also model structure in the light of the domain knowledge of the modelled process.As the primary splitting attribute in the generated regression tree model, the antecedent precipitation index calculated for the period of 5 preceding days API 5 , was chosen.The selection of the API as a primary split attribute was very likely imposed by its definition.The values of the API are defined on the daily time step, whereas other attributes were included into the dataset on the hourly time step.However, the time step definition of the API does not prevail over the further construction of the regression tree since on the second split level other attributes, namely average hourly air temperature during 3 (avgT3) and 14 (avgT14) preceding days, are selected as splitting attributes.
The values of the antecedent precipitation indexes are defined empirically based on the selection of the recession constant, which tend to simulate the drying of the Introduction

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watershed depending on the characteristics of the watershed.From the domain knowledge point of view, the exact values of the API do not offer the exact information about the hydrological nitrate mobilization process traced through continuous streamwater nitrate concentration measurements, however, they provide an insight into the temporal changes of the hydrological state of the Padež watershed responsible for nitrate flushing.
The values of the avgT 3 =10.1 • C and avgT 14 =11.6 • C are from the biogeochemical point of view much more interesting.Temperature together with soil moisture conditions significantly affects the mineralization and nitrification rates in forest soils (Arheimer et al., 1996;Andersson and Lepisto, 1998;Knoepp and Swank, 2002).Whereas maximum mineralization is reported for the forest soil temperature range between 20 and 28 • C (Nicolardot et al., 1994), the mineralization becomes strongly inhibited at temperatures below 10 • C (Knoepp and Swank, 2002).Presuming that air temperatures indirectly address the temperature of the forest soils, the values of avgT3>10.1 • C and avgT14>11.6• C, used for splitting in the regression tree model, define the periods of more effective mineralization, nitrification and nitrate accumulation in forest floors, which is in the periods of changed hydrological conditions available for hydrological mobilization.In Fig. 5 these conditions correspond to the periods covered by branches Nos. 2 and 4.
Figure 7 shows the temporal performance of the regression tree model predicting streamwater nitrate concentrations as regards to the measured streamwater nitrate concentrations during the observed hydrographs.The errors indicate the difference between the modelled and measured streamwater nitrate concentrations.The regression tree model successfully predicts the streamwater nitrate concentrations during spring and summer hydrographs, when the error rarely exceeds 2 mg/l-N.
During the November hydrograph the concentrations of the nitrate were extremely high if compared to other observed hydrographs.Increased exports of the nitrate from forested watersheds are known to occur during seasonal transitions as a consequence of changed biochemical and hydrological conditions (Likens and  • C) and absence of substantial rainfall in the early autumn period (September, October and first half of November), the biogeochemical and hydrological conditions being favourable for accumulation of nitrate in forest soils.Additionally, the vegetation nitrogen uptake is strongly reduced in autumn (Likens and Boremann, 1995;Beachtold et al., 2003).The streamwater nitrate concentrations are not satisfactorily described by the regression tree model during the November hydrograph as the error exceeds 4 mg/l-N.The changes in the nitrate concentrations occurred abruptly, therefore the regression tree model generated using the 125 instances in the leaf pruning criteria is too robust to be able to more accurately describe the streamwater nitrate concentration changes during a single November hydrological event.In order to enable the regression tree to more precisely predict the streamwater nitrate concentrations during the November hydrological and biogeochemical setting we could reduce the pruning factor -number of instances in the leaves, while increasing the risk of overfitting the algorithm to the extreme situation that occurred in November.Furthermore, the dataset included only one such extreme situation, therefore, to improve the regression tree algorithm performance, more autumn hydrological event observations would have to be included into the dataset, as it is the case for spring and summer hydrographs.
The data about the discharge Q and temperature of streamwater T W were not found to be important for the regression tree algorithm; the discharge is considered indirectly through the event water contribution to the total discharge (E W ) in linear regression equations Nos. 8 to 10, which can be found under branches 3 and 4.These two branches cover the part of the dataset which can be characterized as hydrologically moist periods (API5>17.9mm) when the event water contribution to the total discharge can be substantial.It can be seen from the dataset (Fig. 2) that beside some general positive relation between the discharge and streamwater nitrate concentration, similar hydrographs in the sense of the discharge peaks cause various concentration responses.

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It is possible to remove Q, T W and E W attributes from the dataset in order to apply the model for predicting the streamwater nitrate concentrations solely on the API, rainfall and air temperature data as indicators of intermediate hydrological and seasonal variations which control the nitrate flushing responses.Considering the same pruning criteria -125 instances in a leaf, the resulting regression tree performance remains almost unchanged (RMSE=1.03;r=0.90); however, a regression tree model structure is slightly changed in a part where EW was used in the regression tree equations resulting in a larger regression tree with 13 leaves.

Conclusions
Regression trees proved to be a powerful and useful data mining tool in extracting new knowledge from a given database, which helps to review and improve the existent domain knowledge about the mutual seasonal and hydrological controls of the streamwater nitrate pulses.Based on an extensive enlistment of attributes, which were expected to describe a general hydrological and biogeochemical framework of the forested watershed on the temporal scale of more than 50 days of hourly attribute collection, the regression tree generating algorithm successfully described complex streamwater nitrate concentration responses while enabling the conceptual explanation of the resulting regression tree structure.The regression tree model recognized the hydrological and seasonal patterns which lead the forested watershed from the states of being nitrate source limited (early spring hydrographs in March and April), in excess of hydrological mobilizing mechanisms, to the states, when the availability of the hydrological mechanisms was exceeded by the size of the accumulated nitrate in the forested watershed (late spring, summer hydrographs and especially the autumn hydrograph).
However, possible limitations of the regression tree applications were also evident.Due to the extreme and fast streamwater nitrate response and the scarcity of the data in the autumn period (there was only one hydrograph in November) the resulting regression tree model was not able to adequately represent the streamwater nitrate con-

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centrations during the November hydrograph with a given pruning threshold.
The question that remains to be addressed for future applications of the regression tree model is whether a given dataset really contains a range of "typical" hydrological and biogeochemical conditions which could be, through the regression tree generation, recognized and used for the prediction of the nitrate flushing and assessment of the export of nitrate from a forested watershed on different timescales.
streams of the Classic Karst area in Slovenia; the Padež watershed reaches deeply into the hilly area of Brkini in the south (altitude up to 815 m a.s.l.).The studied area consists of Eocene flysch (mainly marl and sandstone layers) underlain by deep cretaceous carbonate bedrocks which also surround the wider area of the Brkini flysch pool.Spatially, the hydrological characteristics of the Padež watershed

Table 1 .
The dataset consisted of 1257 records of attributes which were temporally adjusted on an hourly time step containing 16 hydrographs, and every combination of attributes obtained at Introduction The high nitrate concentrations during the November hydrograph could be assigned to the extremely warm autumn period in 2006 (average daily air temperatures generally around 15

Table 1 .
Wang, Y. and Witten, I. H.: Induction of model trees for predicting continuous classes, Proceedings of the poster papers of the European Conference on Machine Learning, University of Economics, Faculty of Informatics and Statistics, Prague, 1997.Weiler, M. and McDonnell, J. J.: Testing nutrient flushing hypotheses at the hillslope scale: A virtual experiment approach, J. Hydrol., 319, 339-356, 2006.Witten, I. H. and Frank, E.: Data Mining: Practical Machine Learning Tools and Techniques (Second edition), Morgan Kaufmann, 525 pp., 2005.Worall, F., Swank, W. T., and Burt, T. P.: Changes in stream nitrate concentrations due to land management practices, ecological succession, and climate: Developing a systems approach to integrated catchment response, Water Resour.Res.39, 1177-1191, 2003.Introduction Attributes selected for the construction of regression trees.Antecedent precipitation index determined for 3 preceding days prior the day of the hydrograph peak occurrence [mm].API 5 Antecedent precipitation index determined for 5 preceding days prior the day of the hydrograph peak occurrence [mm].API 7 Antecedent precipitation index determined for 7 preceding days prior the day of the hydrograph peak occurrence [mm].API 14 Antecedent precipitation index determined for 14 preceding days prior the day of the hydrograph peak occurrence [mm].Psum 3 h Sum of rainfall during last 3 preceding hours prior the occurrence of hydrograph peak [mm].Psum 6 h Sum of rainfall during last 6 preceding hours prior the occurrence of hydrograph peak [mm].Psum 12 h Sum of rainfall during last 12 preceding hours prior the occurrence of hydrograph peak [mm].Psum 24 h Sum of rainfall during last 24 preceding hours prior the occurrence of hydrograph peak [mm].Psum 48 h Sum of rainfall during last 48 preceding hours prior the occurrence of hydrograph peak [mm].avgT 1 Average hourly air temperature during 1 preceding day prior the occurrence of the hydrograph peak[ • C]. avgT 3 Average hourly air temperature during 3 preceding days prior the occurrence of the hydrograph peak [ • C]. avgT 7 Average hourly air temperature during 7 preceding days prior the occurrence of the hydrograph peak [ • C]. avgT 14 Average hourly air temperature during 14 preceding days prior the occurrence of the hydrograph peak [ • C].