The alerting system for hydrogeological hazard in Lombardy Region , northern Italy : rainfall thresholds triggering debris-flows and “ equivalent rainfall ” method

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The alerting system for hydrogeological hazard in Lombardy Region, northern Italy: rainfall thresholds triggering debris-flows and "equivalent rainfall" method Regarding instability phenomena linked to the hydrogeological risk, the procedure of early warning is based on a comparison of two quantities: thresholds and rainfall, both referred to a defined area and an exact time interval.
2 Thresholds for landslide detachment

Selection of data
The CFMR developed a research study in 2008-2012, considering landslide events with: known moment of occurrence; measured rainfall data; known morphological, hydrogeological and land use data.
The Medium-Low Valtellina has been considered as experimental area, where 52 landslide events (27 of which located in the Valmalenco area) with the above-mentioned characteristics were reported from 1987 to 2003.

Rainfall data
Particular attention has been given to the use of rainfall data: only the rain gauges within 5 km from the landslide event were considered; in case of multiple gauges, the one that showed the best conditions (distance, altitude, slope orientation, rainfall data quality) was chosen.
Because of the lack of knowledge of the value of cumulative rainfall p cum potentially responsible of the landslide detachment, the last 30 days data from the landslide event Introduction

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Full were elaborated to obtain the duration-cumulative rainfall curve p cum (t): this returns the maximum cumulative rainfall p cum observed for each duration t in the last 30 days.
The most marked picks of the p cum (t) curve have been selected as most probable causes of the landslide detachment; each peak has been weighted (with a value between 0.2-1.0)according to its relative upper distance from a regression curves, of the form p cum = αt β , passing through the picks themselves.

Statistical analysis
These rainfall data (t, p cum ) have been analyzed with a weighted stepwise logarithmic multiple regression algorithm, together with morphological, hydrogeological and land use data: local slope i [deg], Curve Number CN (an empirical parameter, developed by the USDA Natural Resources Conservation Service, related with the land cover and the hydrological conditions of the soil), hydraulic conductivity K [cm s −1 ], average annual precipitation AAP [mm].
The purpose was to get an expression in the form c, . . ., t and parameters a, n, m, . . ., q).
The algorithm involves the insertion of a variable at a time within the structure of the formula; after each new variable added, the entire set of variables was subject to a Fisher F test assessment.
The weighting in the algorithm was carried out using the above-mentioned weights.
In Table 1 we reported: for each model: determination coefficient R 2 and increment ∆R 2 of the same with respect to the simplest model (#1); for each variable in each model: regression value, SD and risk level (F test).
Many models have been obtained, but a significant increment of the R 2 could just be reached including (in order) the following variables: time interval t, CN (and its function S; see Sect.The inclusion of average annual precipitation AAP did not help to increase the precision of the regression.
Moreover the hydraulic conductivity K was not considered reliable for insertion in a model, due to the high risk level: the SD is too high compared to the regression value of the variable.

Model and thresholds
The model we choose is the #5 in Table 1.Considering the relationship between S and CN, the equation can be simplified into: (1) In addition to the above model, which represent the critical curve of detachment, we considered appropriate to set lower operational thresholds with a statistical significance; we defined a typical probability of exceedance for each threshold (Fig. 1): moderate (orange): the threshold represent, for each duration, the rainfall causing landslide detachment in the 20 % of cases; ordinary (yellow): the threshold represent, for each duration, the rainfall causing landslide detachment in the 5 % of cases.
The model was found to be the best for several reasons: Introduction

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Full it provides the best increment ∆R 2 and the minimum risk level: i.e. it is very unlikely that the inclusion of parameters within the model is random (due to the limited data), whereas they look well-correlated with the critical detachment p cum values; the limited number of variables makes the model easy for operational use; it's physically coherent: observing the partial variation of the thresholds with respect to the single variables (Fig. 2), the hazard tends to increase in proportion with: local slope i : the higher the slope, the higher the hazard; -CN: the more impermeable the soil, (generally) the higher the hazard.
considering the local variability of soil characteristics, it can be used to draw threshold maps (Fig. 3).

Observed and predicted rainfall: the "equivalent rainfall" method
Ex-post evaluation of ground effects resulting from weather events led to the observation that, for a given rainfall expected, the hazard is substantially greater when the soil is near to saturation.
The CFMR has therefore developed a method to evaluate the hydrogeological hazard, based both on expected rainfall and on observed rainfall in the previous 5 days, which allows to estimate the moisture conditions of soils.Combining the two rainfall quantities, it's possible to obtain an "equivalent rainfall" value to be compared with the early warning thresholds.
This methodology has been implemented within the regional alerting procedure in 2011.Introduction

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Full

Modified CN method
The equivalent rainfall method is derived from the Curve Number method (CN method), introduced in hydrology to estimate the surface runoff of a basin after a rainfall event, modified by Singh (1982) and Mishra et al. (2004Mishra et al. ( , 2006)).
The modified CN method is based on a balance equation: with the following variables, expressed in mm: -P = total rainfall; Each basin portion, according to its characteristics (land use and classification, condition of superficial soil), presents a typical CN value.This allows to estimate the maximum potential retention S [mm] of the soil, which includes all hydrological losses: S = 25 400 CN − 254. (5) The antecedent moisture conditions (AMC), used to increase/decrease the CN, can be obtained considering the antecedent rainfall.There's not an explicit indication about how many days to consider, but a well-established practice (recommended by the National Engineering Handbook of NRCS) suggests the last 5 days rainfall (P 5 [mm]) in order to choose among three discrete classes: I (dry), II (normal) and III (wet).Introduction

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Full This modified method is based on the assumption that runoff coefficient C, defined as ratio between net runoff and net rainfall, coincides with the degree of saturation Sr of the soil: and requires the validity of the two following hypotheses: where λ is the coefficient of initial abstraction (usually taken between 0.05-0.2).Combining these equations with the balance equation (Eq.4), the total runoff is expressed as: Assuming that the soil is in dry conditions before the 5 day interval, the following equation allows to estimate the M term as a function of the rainfall P 5 :

The "equivalent rainfall" method formulation
The modified CN method can be used to estimate the hydrogeological hazard of a basin portion.Assuming the hazard degree to be proportional to the degree of saturation Sr of the soil, we could define the "equivalent rainfall" P eq , associated with the Introduction

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Full predicted rainfall P , as "the predicted rainfall on the local dry soil necessary to cause a Sr equal to the one caused by the rainfall P preceded by the rainfall P 5 ".
Combining the above equations (Eqs.9 and 10) we obtained the system of equations to derive the P eq : That is, the same Sr will be caused: by the predicted P , after the observed P 5 ; or by the predicted P eq on local dry soil.
Even in the absence of predicted rainfall P , the "base equivalent rainfall" P eq0 (function of CN and P 5 ) stands for the worsening in hydrogeological hazard due just to the antecedent rainfall.Thus, the equivalent rainfall value is deemed more appropriate to indicate the hydrogeological hazard and should be compared with the threshold values.
It should be pointed that, when the assumption of dry soil before the 5 day interval is not acceptable, the same time interval can be properly increased.
The above described model is now included in the regional technical legislation (2008,2011,2013).
Further observations have shown that it is appropriate to give more importance to the most recent rainfall: it was found an empirical relationship that defines a weight π j for the daily cumulated rainfall P j of the j th day (j = 1, . .., 5) prior to now.Thus P 5 is given by a weighted sum: Introduction

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Full Currently it is used a value of 0.8 for the parameter β.
In Fig. 4 a graph shows the dependence of the base equivalent rainfall P eq0 from CN and P 5 , in the hypothesis that each weight π j is equal to 1.
It can be observed that the higher the CN, the lower the P eq0 : on mostly impermeable soil the infiltration rate is low and Sr (and therefore C) tends to approach quickly to the unit, mainly independently from the antecedent rainfall.

Discussion
The rainfall thresholds, obtained as described in Eqs. ( 1)-( 3), and the equivalent rainfall method can be combined to evaluate the hydrogeological hazard.
Operationally the CFMR has created an automated system for the creation of hazard maps in real time, to allow a comparison of the equivalent rainfall with the thresholds.
The Lombardy region has been divided into computational domains of 1 km 2 , on each of which: the threshold values, for each duration, are defined; the predicted equivalent rainfall is hourly computed, using: observed rainfall data: PRISMA data (i.e.RADAR data corrected with the observed data from stations on the ground, Fig. From the comparison between equivalent rainfall and thresholds, hazard maps are obtained with the hazard levels (Fig. 6): each single domain is colored according to a standard color scale (green-yellow-orange-red stand for absent-ordinary-moderatehigh hazard).
From the observation of the distribution of hazard, the evaluation of vulnerable elements and potential emergencies in progress, the CFMR proceed to a summary in order to alert different "homogeneous areas" (Fig. 6), as required by the national (2004) and regional (2008,2011,2013) legislation.

Conclusions
In the next future the critical detachment model will be subjected to a critical evaluation: the limited data used for the analysis and the inaccuracy of the time of occurrence of landslide events necessarily introduced uncertainty to the results.
In addition, a more accurate analysis on the role played by each parameter will be conducted.
The former equivalent rainfall method (Eq.11) is now included in the regional technical legislation, but the calibration of the weights of the observed rainfall (Eq.12) and other future improvements depend on the observation of its consistency in the alerting system.
The described approach has been used for a "homogeneous area" scale alerting, but recently the CFMR has implemented the method with the creation of localized alert documents, focused to limited portions of the region (typically at the scale of a river basin or less).This would be: more efficient, because it considers the local variability of rainfall and soil characteristics; Introduction

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Full Functional Centre (CFMR) of the Civil Protection of the Lombardy region (North Italy) has the main task of monitoring and alerting, particularly with respect to natural hazards.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 3.2) and local slope i .Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 5), computed by ARPA Lombardia-SMR (Agenzia Regionale per la Protezione dell'Ambiente -Servizio Meteorologico Regionale); forecasted rainfall data returned by meteorological models (such as COSMO-I7, Fig. 5); Discussion Paper | Discussion Paper | Discussion Paper | local soil characteristics, approximately summarized by the CN.

Figure 5 .
Figure 5. Example of observed rainfall data (PRISMA: RADAR corrected with observed data from stations on the ground) and forecasted rainfall data (COSMO-I7 model).