EVENT'S CHARACTERIZATION
MODEL FOR THE CLASSIFICATION OF ORDINARY AND CRITICAL RAIN-BASED WEATHER AND CLIMATE EVENTS AND MODEL FOR THE REMOTE MONITORING OF THEIR GROUND EFFECTS CREATED IN A GIS ENVIRONMENT
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INTRODUCTION
In a generic territorial context, whose morphology and climate remain constant over time and in conditions of tectonic calm, the flow pattern of any meteorological/climatic event of a rainfall nature presents recurring characteristics in time and space, called peculiarities.
These peculiarities permict us to dentify and recognize if the event has already occurred in the past or is expected to occur in the near future.
The peculiarities of the event are highlighted by the geometries of the event that are examined during its evolutionary cycle that is understood as a succession of event geometries over time.
Succession of event’s geometries are analyzed in the three dimensions of space as well as in the time interval during which it occurs.
A drainage basin can be considered a structure that operates consistently over time in the drainage of surface waters until the physical territory is modified by exogenous, endogenous, or anthropogenic agents.
If we consider the interaction between the precipitations and the physical territory, in a context in which the basin's morphology remains constant, the main process variables include the volumes of water falling within it, i.e., inflows.
In this context so the geographical and/or spatial distribution of inflow water’s volumes and the variation in their geographic and/or spatial distribution over time or during the evolution of an unfolding meteorological/climatic event could be considered so as variables.
The following discussion proposes a model for characterizing these events based solely on the analysis of the spatial and temporal distribution of inflows in delimited and divided territorial contexts.
The territory is divided using various criteria and through differents analysis grids, in smaller territorial units, in order to obtain spatial, geographic references that allow us to define the specific characteristics of such events.
It is also important to divide the event’s evolutionary cycle in time intervals using appropriate time’s units so to have time’s references too.
The peculiarities of a generic event, whether meteorological or climatic, are given by its geometries, called event geometries, understood as the geographic distribution of inflows at the generic instant Tx of the ongoing event and defined at each instant during which the event occurs.
The peculiarities, furthermore, are given by the evolutionary cycle of the event, understood as a continuous succession of event geometries over time, which occurs in a time interval between a start time T0 and a cessation time Tf.
Although they may seem arbitrary, they are nevertheless subject to predefined rules.
The reconstruction of the evolutionary cycle of a generic event, through its geometries, in a known time interval is called event reconstruction, and each step is performed both on the horizontal plane (plan view) and along the vertical direction (elevation).
Finally, the proposed model can represent the evolutionary cycle of a generic event in a graphical summary.
This can be used as a tool for analyzing, comparing, and classifying weather and climate events of any nature.
It can also be used to verify the occurrence of an event, even a catastrophic one, and the resulting damage by determining all the characteristics that make it unique and distinguish it from other events.
These characteristics, therefore, allow us to recognize it if it has already occurred in the past or is expected to occur in the near future.
1_ANALISYS CRITERIA AND TOOLS
The drainage basin can be considered as a structure that operates consistently over time in the drainage of surface waters as long as the physical territory is not modified by exogenous, endogenous or anthropogenic agents.
1.1 THE HYDRAULIC PATH
In the proposed model, a generic hydraulic path along a slope refers to the most likely flow path for precipitation flowing to the surface along that slope.
Let's consider a generic portion of a parallel slope delimited upstream by a watershed line and downstream by a drainage line.
FIG_1
FIG_2
Let us consider a generic point A located along the watershed line and, from that point, let us also consider a generic mass of water that precipitates and flows to the surface following a path, called hydraulic, which develops along the slope and ends at point G located along the watershed line.
FIG_3
In the proposed model, the hydraulic path follows the directions of maximum slope along the considered slope section.
Therefore, given a starting point located along the watershed line, its path can be defined by following very specific construction rules.
Draw the tangent to the watershed line at point A and then draw the perpendicular to the tangent at A.
This latter line represents the direction of maximum slope originating from point A.
This line also intersects the contour line located immediately downstream of the watershed at point B (contour line 45 meters above sea level in FIGURE 3).
Once point B has been identified, the same actions performed for A are repeated, thus identifying the direction of maximum slope starting from point B.
This intersects the contour line immediately downstream at point C, and for this point, the same actions performed for A and B are repeated.
This reconstructs a hypothetical hydraulic path starting from A and ending at point G, located along the drainage channel.
FIG_4
In general, by following the construction rules on paper, it is possible to identify numerous hydraulic paths that develop along the stretch of parallel slope considered.
1.2 DRAINAGE
In the proposed model, water-physical land interaction processes include both the drainage of excess precipitation that flows to the surface and all those processes in which precipitation plays a significant role, such as landslides and other gravitational processes.
Generally, these refer to all hydrological and geomorphological processes that are activated during the occurrence of a generic weather/climatic event.
In a generic territorial context, whose morphology remains constant over time, the surface drainage processes of excess rainfall maintain recurring geometric characteristics over time until tectonic, climatic, geomorphological, and/or anthropogenic factors intervene to radically alter the geomorphological structure.
Radical changes in the morphology of the territory include all those changes that lead to a radical variation in the trend of the hypsographic/hypsometric curve of that generic territorial context.
Consider a generic portion of land devoid of vegetation, free of any human influence, and whose substratum is completely impermeable.
In this context, precipitation partly evaporates and partly flows to the surface. This portion of land is depicted on the map by contour lines.
Consider a generic portion of land devoid of vegetation, free of any human influence, and whose substratum is completely impermeable.
In this context, precipitation partly evaporates and partly flows to the surface. This portion of land is depicted on the map by contour lines.
FIG_5
FIG_6
Surface water flows along defined hydraulic paths controlled by the morphology of the investigated terrain. In general, surface water flows along the slope with the greatest slope gradient.
FIG_7
Let us now consider this portion of land during time T1 of a generic rainfall event.
The morphology of the topographic surface is described in plan view by the contour lines, while the geographic distribution of precipitation heights at time T1 is described in plan view by the isohyets.
FIG_8
Now consider the intersection points between the isohyets at time T1 and the contour lines.
At these points, the elevation of the topographic point and the precipitation depths at time T1 are known.
FIG_9
A portion of this precipitation is returned to the atmosphere through evaporation, while the excess flows to the surface.
Now consider the excess water flowing to the surface. Regardless of its quantity, in the territorial model described above, these waters, by definition, follow the directions of maximum slope along the slopes up to the reference drainage basin, from where they continue to the outlet section of their catchment area.
Now consider the generic point P on the topographic surface of this territorial context, located along a generic contour line.
FIG_10
During each meteorological event, an isohyt certainly passes through this point, indicating the height of precipitation that falls here.
By repeating the operations described above, it is possible to define the direction of maximum slope for this point P and a hypothetical hydraulic path that starts from here.
FIG_11
During a meteoric event, consider the arrangement of the isohyets at time T1.
In particular, consider the isohyet passing through the generic point P, regardless of the indicated precipitation depth.
At this point, the elevation and the hypothetical precipitation depth falling there are known, as well as the direction of maximum slope of a hypothetical path starting from this point and continuing along the slope.
FIG_12
As the event unfolds, its characteristics change, and with them the pattern of the isohyets changes, but the morphology of the territory within which the event occurs does not so significately so as defined before
FIG_13
FIG_14
FIG_15
Specifically, the isohyet passing through the generic point P on the topographic surface changes.
It is assumed that the elevation at this point remains constant, and it is also assumed that the direction of maximum slope of the hypothetical route starting from here also remains constant.
In the examples described above, it is assumed that there are no radical and significant changes to the morphology of the portion of land investigated and described by the contour lines.
So during the event the drainage process of the water flowing to the surface presents a defined geometric structure that remains constant over time until the morphology of the area undergoes significant changes.
In general, given a generic territorial context, this will operate consistently in the drainage of surface water until anthropogenic, geomorphological, tectonic-structural, and/or climatic factors and/or processes bring about significant changes to its morphology.
1.3_SUBDIVISION OF PRECIPITATION WATER
Given a generic section of slope, this, during rainfall events, will always react in a given way to the stresses induced by even critical rainfall events, which is a function of its geomorphological, hydrological, and hydrogeological characteristics. In this sense, let's consider a generic section of slope located along the slope as shown in Figure 16.
FIG_16
FIG_17
FIG_18
This portion of land, during a rainfall event and barring significant changes in its morphology, will drain excess water—that is, water that does not evaporate or infiltrate—always in the same manner and always along predefined hydraulic paths or routes.
The model proposed in the following pages is based on this assumption.
This process is repeated until the morphology or the aforementioned characteristics of the portion of land under consideration are modified due to endogenous, exogenous, and/or anthropogenic causes.
FIG_19
FIG_20
Let's consider a generic portion of physical territory whose substratum is impermeable.
In this context, the perpendicular rule applies, and all the water that precipitates at, for example, a generic point P, located along the generic contour line H3, tends to flow to the surface along the path or hydraulic route that originates from that point.
Now consider what can happen when a generic amount of precipitation water, expressed in water height hPx, hits the ground at a generic point on the Earth's surface that is not impermeable.
At P, first of all, the elevation Hx is known, as are the slope and the hypothetical direction of flow "d" of the excess water, which correspond to a percentage or fraction X of hPx: D = X x hPx or D = XhPx%.
Furthermore, based on the hydrogeological characteristics of the soil or rocks of the substrate, the values of the infiltration factor, or the percentage or fraction Y of hPx that infiltrates, are or will be known: I = Y x hPx or I = YhPx%.
Finally, based on the climatic characteristics, the parameters AVERAGE PRECIPITATION and AVERAGE TEMPERATURE typical of the area under investigation are or will be known, allowing us to define the extent or values of the evapotranspiration process, expressed as a percentage or fraction Z of hPx: ET = Z x hPx or ET = ZhPx%.
At point P, therefore, the following parameters will be known or can be defined:
At P (Hx, slope, d, hPx)
At P (Hx, slope, d, XhPx%, YhPx%, ZhPx%)
2_METEOROLOGICAL EVENT AND CLIMATE EVENT
AT THE CURRENT STATUS OF THE WORK, THE FOLLOWING DEFINITIONS OF METEOROLOGICAL EVENT AND CLIMATIC EVENT ARE ADOPTED
WEATHER EVENT
“……a set of short-term changes in pressure, temperature, humidity, precipitation, solar radiation, wind,…….”
CLIMATE EVENT
"...average weather pattern in the troposphere, the variation of seasons, and temperature extremes in a region, considering a period of at least 30 years..."
3_ANALYSIS GRIDS
In the proposed model, the event’s geometry or the geographic distribution of inflows during a generic stage of the evolutionary cycle of a rainfall and/or climate event is determined using reference territorial units defined by analysis grids.
For the purposes and requirements of this work and in the reported application cases, conformal and/or functional analysis grids were used.
These were constructed taking into account the morphology of the basin and the possible geometries of the water-soil interaction processes.
Overall, they allow for fewer steps to be performed during the event characterization process and, therefore, serve the required function well.
An example of these grids is those constructed by discretizing the territory under examination by elevation bands.
Generally, these are grids whose elements are represented only by the elevation bands of the hydrological system being analyzed.
The choice to use grids whose elements are given by elevation ranges or that take elevations into account is also justified by the fact that climate and meteorological parameters vary not only with latitude but also with elevation.
In general, any type of analysis grid can be used to characterize a weather/climatic event: grids consisting of Thiessen polygons, grids with boundaries between slope classes, pixels, meshes, geological boundaries, square grids, etc.
Dividing the territory into square finite elements, for example, allows for characterization of the event but is not functional as it requires additional steps to reconstruct the event along the elevation. Furthermore, these grids are non-compliant as they do not take into account the morphology of the territory.
4_EVENT GEOMETRIES AND EVENT RECONSTRUCTION
By dividing the investigated area into smaller territorial elements, the analysis grids determine the precipitation height Px within each unit at the generic time Tx.
Given the surface area of the grid units Ax, the inflow volume, defined as the volumes of water Vx falling within those units at the instant or time interval considered, is also determined.
The flat representation of the geographic distribution of the volumes of water falling within the various grid units at the generic time Tx of the event represents the geometry of the event itself at the instant or time’s interval considered.
The flat representation, in chronological order, of multiple event geometries relating to the various phases of the evolutionary cycle of the analyzed phenomenon represents the reconstruction of the event over time.
For each event geometry represented on the horizontal plane, corresponding graphical solutions/graphs also describe or characterize it along the vertical direction or along the altitude.
A single event geometry therefore represents the spatial or geographic distribution of inflows within the basin under consideration and, in this context, the evolution of the event is described by multiple event geometries that indicate the variation over time of the geographic or spatial distribution of the volumes of water precipitated within the catchment area.
5_GRAPHIC SUMMARY SOLUTION FOR THE ANALYSIS, COMPARISON AND CLASSIFICATION OF METEOROLOGICAL AND CLIMATIC EVENTS
The analysis and characterization processes aim to define spatial, temporal, and quantitative references that allow us to identify, through its specific characteristics, each meteorological event in order to recognize it if it has already occurred in the past or is expected to occur in the future.
To this end, a summary document is constructed for the analysis, comparison, and classification of weather and climate events.
In the proposed model, the characterization process is considered complete when the areas of the individual units of the analysis grid adopted and the precipitation inflows within them are compared in a scatter plot.
This step allows us to construct the main summary document of the model under discussion, as it allows us to define the temporal and quantitative reference limits.
In a scatter plot, for each event geometry, the area values of the individual units of the analysis grid employed are plotted along the X-axis, while the volumes of the corresponding inflows at the generic time point Tx are plotted along the Y-axis.
This results in a graph or graphical solution that represents the event's geometries and its evolutionary cycle, allows for analysis of the event represented, allows for comparison with past and future events, and allows for classification of the event occurring within the basin.
6_METHOD
To illustrate the points made in this paper, several case studies were used, both current and ongoing, and an analysis grid was created by discretizing the investigated areas into smaller reference territorial units, applying various criteria.
The investigated territorial areas are represented by four hydrographic basins: the "Rio Maggiore" or "Fosso della Rustica" basin, the "Fosso Cupo" basin, the "Marta River" basin, and the "Tiber River" basin.
The first three are located in similar territorial and climatic contexts, while the "Tiber River", in its surface area, is characterized by strong and marked morphological and climatic differences.
"FOSSO CUPO"
The Fosso Cupo is a left-bank tributary of the Rio Maggiore or Fosso della Rustica, itself a right-bank tributary of the Tiber River. It extends for approximately 14 km2 in a north-northwest-south-east direction, between the municipalities of Gallese (VT), Orte (VT), and Vasanello (VT).
The drainage basin lies between an altitude of 311 m above sea level in the "Casa Porchiaroni" area of Orte (VT) (Coord.: 284527, 4702222; ED_1950_UTM_ZONE_33) and an altitude of 67/65 m above sea level. near Monticello, just east of the historic center of Gallese (VT) (Coord.: 287334, 4694608; ED_1950_UTM_ZONE_33).
The entire area falls entirely within the province of Viterbo (VT) and also falls within sheet number 137 Viterbo of the Geological Map of Italy (I.G.M. scale 1:100,000).
Regarding cartographic references, the basin is variously distributed within the following topographic sections (C.T.R. 1:10,000 Lazio Region): Magliano Sabina 356020, Gallese 356010, Vasanello 346130, and Casa Trippetti 346140.
FIG_21
THE ANALYSIS GRID AND THE CLIMATE EVENT
In this case, the calendar year was considered the climatic event, and for each month, the corresponding event geometry was reconstructed on the plane, integrated with graphical solutions that also describe it along the elevation.
The analysis grid construction criteria take the elevation factor into account, but the grid units are not elevation bands but rather sectors of the drainage basin at predefined elevations.
That is, given the main route of the hydrographic network, a generic number of hydraulic sections were identified along it at known elevations, from which the corresponding ridges branch off.
The areas between two of these consequent ridges constitute the sectors or units of the analysis grid.
This results in a compliant and functional analysis grid consisting of sectors that follow one another with elevation and delimited by ridge sections of the sections located at known elevations.
For each territorial unit obtained, the surface area was defined, the monthly average rainfall values were obtained, on a thirty-year basis, from the data made available by various public bodies (Lazio Region hydrological annals and ARSIAL data).
So finally, for each unit, the relative regime of the monthly average inflow values was defined.
FIG_22: FROM THE HYDROGRAPHIC NETWORK I EXTRACT THE MAIN COLLECTOR AND IDENTIFY THE POINTS OF INTERSECTION WITH THE CONTOUR LINES. THESE POINTS ARE HYDRAULIC SECTIONS OF WHICH THE ALTITUDE ELEVATIONS ARE KNOWN. THE MAIN COLLECTOR IN THIS CASE IS REPRESENTED BY THE LONGEST PATH.
FIG_23: FOR EACH POINT IDENTIFIED I TRACE THE SECONDARY WATERSHED AND IDENTIFY THE SECTORS OR SUB_UNITS OF THE RIVER BASIN.
FIG_24: EACH SECTOR HAS ITS OWN SURFACE EXTENSION
HYPSOMETRIC CURVE AND INCREASE IN THE AREAS DRAINED BY THE MAIN COLLECTOR
To compare the areas drained by the main collector and the increase in the basin surface area as one moves from upstream to downstream, I construct the hypsometric curve according to the classical criteria and report in the same graphic solution the normalized values of the former with respect to the maximum value or with respect to the basin area, since at the closing section of the basin the main collector drains 100% of the catchment area.
FIG_25: HYPSOMETRIC CURVE COMPARED WITH THE CUMULATIVE AREA OF THE SECTOR SURFACES
Given a generic elevation expressed by the corresponding contour line, along which there are NIz drainage sections, including the main collector, considered the longest route of the hydrographic network.
Considering the contour line set at h = 0.6 (approximately 210 meters above sea level) in the graphic solution of Fig. 25, this presents an upstream catchment area for the NIz sections equal to approximately 61% of the entire basin surface area, a value estimated along the hypsometric curve in the graphic solution of Fig. 25.
The main collector alone drains 40% of the basin surface area at the same elevation; therefore, there is a significant difference between the basin area drained by the main collector alone and that of the remaining hydraulic sections.
In the specific case of h = 0.6, the difference is equal to 2666700.726 m2, or approximately 20% of the catchment area. This area represents the drained area or the intake area of the NIz sections – 1 (main collector) located along h = 0.6, or approximately 210 meters above sea level.
Considering a monthly average value of precipitation height uniformly distributed for the month of November equal to 110 mm which converted into meters would be 0.11 meters within the surface located upstream of altitude 0.6, approximately V = 0.11 x 2666700.726 = 293337.08 m3 of water falls and of these 117334.832 m3 (40%) flow through the main collector while the remaining part is divided in various proportions between the NIz sections – 1 (main collector) located along the altitude 0.6 in the graphic solution of Fig. 25.
CLIMATIC CHARACTERISTICS AND INFLOW REGIME
The Fosso Cupo basin extends over a limited altitude range (approximately 244 meters), and therefore no marked variations in climatic characteristics can be identified between one climatic zone and another or between one sector of the analysis grid and another.
From the analysis of the available and derived data, it is noted that the wettest month within the basin is November, while the driest is July.
Furthermore, it appears that the trend in average monthly precipitation within the various sectors is extremely variable, with a general tendency to increase in the valley sectors throughout the calendar year.
The basin under examination falls within a broader territorial context characterized by a sublittoral-Apennine rainfall regime (Tonini 1959, Minella 1967), with a very dry summer quarter (May, June, July) and an autumn quarter (September, October, November) characterized by abundant rainfall.
The investigated catchment area similarly experiences a dry or arid summer period characterised by low average monthly rainfall values of around 30 mm in the month of July and an autumn period with average monthly rainfall values exceeding, in every sector, 100 mm in the month of November.
CONFRONTO_PRECIPITAZIONI_AFFLUSSI.pdfFIG_26:
PRECIPITAZIONI_AFFLUSSI.pdfFIG_27:
Comparing the geographic distribution of monthly mean precipitation levels with the geographic distribution of the corresponding inflowing water volumes throughout the year highlights the fact that the former are extremely variable both in space and time, or throughout the year, while the precipitating water volumes exhibit recurring geographic distributions over time. Indeed, the maximum and minimum values always fall within the same areas, as do the intermediate values.
7_SPATIAL, TEMPORAL, AND QUANTITATIVE REFERENCES
THE SUMMARY DOCUMENT
In the proposed model, the characterization process is considered complete when the areas of the individual units of the adopted analysis grid and the inflows precipitated within them are compared in a scatterplot.
This step allows us to construct the main summary document of the model under discussion, as it allows us to define the temporal and quantitative reference limits.
In a scatterplot, for each event geometry, the area values of the individual units of the employed analysis grid are plotted along the X-axis, while the volumes of the corresponding inflows at the generic time point Tx are plotted along the Y-axis.
For a single geometry, a cloud of points is obtained arranged around a trend line passing through the origin. This last point is given by the apex of the watershed or the elevation range near it where the area is equal to or tending to zero, and consequently the inflow value is also equal to or tending to zero.
Each individual point has as its coordinates the area of the elevation range or reference unit considered and the volume of water precipitated in it at time Tx.
The slope of the trend line is given by the ratio between the change in volume and the change in area of the reference units and is equal to a height. This value indicates the average value of precipitation height if it were uniformly distributed within the basin.
FIG_28:
CHARACTERISTIC ELEMENTS OF AN EVENT'S GEOMETRY
Therefore, within each territorial context, each event geometry presents characteristic elements that allow it to be distinguished from others or recognized if it has already occurred in the past or is expected to occur in the near future.
In fact, within a generic, appropriately discretized territorial context, event geometries can recur with similar, if not identical, characteristics even during the course of a single weather/climate event.
In the summary document and in the representation of the event geometry referred to a generic time point Tx of a generic event, two characteristic elements are distinguished: the angle α that the trend line forms with the X-axis and the corresponding angular coefficient m.
Among these, the second element, as previously mentioned, represents the value of the precipitation height falling at time point Tx within the investigated territorial area, if it were uniformly distributed there.
EVENT RECONSTRUCTION
The reconstruction of a generic weather-climatic event, therefore, is achieved through the representation in the same graphic solution of multiple geometries of the event itself in chronological order and arranged between the Ti start time and Tf cessation time of the event.
FIG_29:
At the latitude of the cases under examination, the driest month is July, while the wettest or humid month is November. The average monthly rainfall and inflow values of these two months include all the other values relating to the other months of the year.
FIG_30:
The month of July represented in the Volumes_Areas graphic solution provides the aridity or "dry" limit, while the month of November provides the humid or "wetted" limit. The point clouds for these two months also include those for all other months.
Each point cloud corresponds to a trend line with the characteristics described above, and each point cloud also corresponds to an event geometry.
Therefore, based on the latitude and elevation of the basin under consideration, the graph area is divided into three sectors: one is below the "dry" limit, one is between the "dry" limit and the "wetted" limit, and the third is above the "wetted" limit.
Among these, the sector between the two limits represents the sector of frequent inflows (an inflow regime consolidated over time) or event geometries characteristic of the basin throughout the year, while the other two sectors represent the range of infrequent or less frequent and/or little-known inflow values.
A persistence of event geometries below the dry limit indicates arid conditions, while a persistence of event geometries above the wetted limit indicates exceptional, critical, and little-known conditions.
From these two limits, referring to two distinct event geometries, I extract the limit values for mean precipitation height in the case of values uniformly distributed within the basin by calculating the angular coefficients of the trend lines.
Knowing the area values of the reference grid units, we can proceed in reverse and define arbitrary limits by assuming a uniform distribution of precipitation depths within the basin—for example, 10 mm, 50 mm, 100 mm, and so on.
In general, comparing and representing the parameters considered within the adopted graphical solution provides initial indications of the temporal and quantitative limits to be used as a reference for assessing current, past, and future events.
In the case of evolving events, comparing the sequence of event geometries on the plane and comparing them in the graphical solution with a known event whose effects are known allows us to determine whether the current event exhibits the same characteristics.
When working with forecast data, particularly weather data, we can proceed in the same way. By comparing the evolutionary cycle of the forecasted event both on the plane and in the graphical solution, we can similarly attempt to determine its effects.
CHARACTERISTIC ELEMENTS IN EVENT’S RECONSTRUCTION
The characteristic elements in an event reconstruction are given by the angles that the trend lines of the event geometries, which occur during the course of a generic event, form with the X-axis.
The angle β between the trend lines relating to the "dry" and "wetted" limits also represents a characteristic element.
Another characteristic element is the maximum value of the surface area of the reference territorial units into which the investigated area has been divided, indicated as the "maximum area" in the graphical summary solution.
All the characteristic elements, both of the individual event geometries and of the event reconstructions, allow us to characterize each individual weather and climate event that occurs within a generic, appropriately discretized territorial context.
During the course of a generic event, event geometries may recur with the same characteristic elements. Specifically, those describing critical geographic distributions of inflows, or those inducing a severe hydrological-geomorphological response, may also recur.
Contiguous or adjacent portions of land may exhibit similar characteristic elements if the local climate and morphological characteristics of the investigated areas are similar, but they are never identical because, even under the same meteorological-climatic conditions, the geomorphological context differs, even subtly. Therefore, "THE HYDROLOGICAL RESPONSE" varies spatially and is, in fact, called "LOCAL."
FIG_31:
In general, based on the cases analyzed, we can hypothesize that the characteristic elements are a function of the geomorphological and rainfall characteristics of the investigated area, and therefore their values vary as these factors vary.
It is possible that the same values may be found in two or more geographical areas, even non-contiguous ones.
For example, consider two large flat areas (same morphology) characterized by the same rainfall regime (same rainfall regime), or, if not identical, similar ones.
Consequently, these two portions of territory could present similar, if not identical, characteristic elements.
That is, the proposed model hypothesizes that, considering only the spatial factor, the characteristic elements are specific to a given area, but they may also recur in non-contiguous areas or locations.
CLIMATE AND TOPOGRAPHY
The values of inflowing water volumes depend on the area values of the reference territorial units considered (TOPOGRAPHY FACTORS) and the values of precipitation heights (CLIMATIC FACTORS).
Within a generic territorial context, the inflowing volume parameter is a function of the area values of the reference territorial units and the values of precipitation heights, which vary over space and time, even during the occurrence of a generic meteorological/climatic wind.
Within this territorial context, the area parameter of the reference territorial units, however, should be considered an independent variable, or at least one that depends on other factors called topographic factors, which will be discussed later.
In general, therefore, the trend lines and consequently the values of their angular coefficients are susceptible to variations over time and space as the variables precipitation height and area of the reference territorial units change.
CLIMATIC FACTORS
Given a generic basin and assuming that the values of the "ai" parameter, representing the areas of the reference territorial units, remain constant over time, then variations in the position of the "dry" and "wetted" boundaries are attributable exclusively to variations in the values of the variable hp (precipitation depth) over time and space.
Specifically, the characterization of the calendar year's climate event is carried out through the analysis and use of monthly mean precipitation depths, which, together with other parameters, help describe the local climate characteristics or the territorial context being analyzed.
In this case, the monthly mean precipitation regime was considered, whose variations over time are attributable to ongoing climate change and are difficult to determine, while their spatial variations are known.
Indeed, a global analysis of the data from the cases examined revealed that the positions of the "dry" and "wetted" boundaries, defined by the aforementioned characteristic elements, are a function of the geographical position of the investigated territorial context, and this aspect, in fact, is a consequence of the variation in the local climate, which varies with the geographical position.
TOPOGRAPHY FACTORS
In the proposed model, the TOPOGRAPHIC FACTORS of a generic portion of territory are all those factors that define its geomorphological context and whose changes over time result in a radical change in its morphology.
Changes in the TOPOGRAPHIC FACTORS over time are highlighted by radical changes in the trend of the hypsometric curve of that portion of territory.
In the proposed model, the geomorphological aspects have been highlighted by reporting the surface area parameter of the reference territorial units in the summary graphic solution, and this parameter also affects the values of the tributary water volumes.
In general, therefore, topographic factors are those factors that are sensitive to those processes capable of altering or modifying the trend of the hypsometric or hypsographic curve of a generic catchment area or a generic portion of territory and which therefore affect the area parameter in the calculation of inflow values.
In the proposed model, TOPOGRAPHY FACTORS are considered to include geomorphological, tectonic, and structural aspects, as well as anthropogenic aspects of a given portion of land.
Regarding the former, consider the normal "WILSON" evolutionary cycle, in which continuous erosive activity, occurring within a given basin through the erosive and depositional processes of surface runoff, as well as through mass movements and other processes, results in a continuous change in the hypsometric curve.
In fact, in this evolutionary context, based on the trend of this curve, a distinction is made between young morphology, mature morphology, and senile morphology.
Regarding anthropogenic aspects, consider, for example, the shaping effect of intense mining activity capable of significantly modifying the profile of a relief and, consequently, its hypsometric curve.
The tectonic and structural aspects of a given portion of land can control both its morphology and the geometric layout of its drainage network.
In general, a tectonic-structural event, even a mild one characterized by weak horizontal and vertical displacements, controls the spatial distribution of the surface extension values of the elevation bands that constitute that portion of land and therefore also controls the trend of the hypsographic and hypsometric curves.
ANALYSIS OF A GENERIC EVENT
Once the territorial area under examination has been divided into smaller, functional units, based on the investigation criteria adopted in this model, a generic climatic weather event, including a critical one, is studied on the horizontal plane.
For each smaller unit of the constructed analysis grid, the mean precipitation value(s) falling therein is assessed at regular intervals. Based on these, the inflows, defined as volumes of water, preferably expressed in cubic meters, are calculated.
Measurement at regular intervals is performed by dividing the period of time during which the event occurred or is occurring into smaller, regular intervals. The duration of these intervals depends on multiple factors, including the characteristics of the available data.
Hydrological annals, for example, provide both hourly and daily data for each recorded event.
Depending on the characteristics of the event being analyzed, which may last less than or greater than a day, one or the other can be used.
Once the time interval to be used has been chosen, during the analysis phase, the geographic distribution of inflowing water volumes within the reference analysis grid is defined horizontally.
The proposed model is based on the assumption that each rainfall-type weather and climate event is considered unique and peculiar if only the spatial-temporal distribution of precipitation heights is considered, but recurrent if the spatial-temporal distribution of inflows, defined as the volumes of water falling within the investigated territorial area, is considered.
HORIZONTAL EVENT ANALYSIS
Based on the above assumptions, the precipitation height variable is considered extremely variable in space and time and, therefore, difficult to control, while the water volume variable is easier to control.
For a generic basin, having defined the analysis grid on the horizontal plane, it can be assumed that if the morphological characteristics of the basin do not radically change over time, the catchment area responds to weather and climate impulses in similar and recurring ways when similar and recurring events occur.
Similar characteristics refer to the geometric characteristics of the interaction processes between precipitation and the physical territory, described through the geographic distribution of inflowing water volumes within the constructed analysis grid.
In general, it is assumed that weather and climate events described through the geographic distribution of inflows within a reference analysis grid correspond to a similar, if not identical, hydrological response, also called local because it differs from basin to basin.
In summary, the geographic distribution of inflows at each instant is called the event geometry, and their sequence over the time interval during which the weather event occurs is called the event reconstruction.
If two events have identical event reconstructions, they are said to be equal and recurrent, while they are said to be different if their event reconstructions differ radically.
Among the extreme cases are similar and dissimilar cases.
In the proposed model, a recurrent event is recognized if, when compared, two events have equal or very similar event geometries at each instant, or if they have the same event reconstruction.
Given a known critical event that occurred in the past, its reconstruction is performed as previously described and it is assumed to be the reference event.
For this event, the relevant event code is defined, given by the name of the location where it caused the greatest damage and the date it occurred.
For each basin, based on its recent history, it can be assumed that there may be multiple known events and therefore multiple reference events.
For a critical reference event, furthermore, its event reconstruction is performed on the horizontal plane as described above, followed by the creation of a summary graph and other graphic solutions that provide a complete picture in a three-dimensional spatial context.
The event geometries, i.e., the event reconstruction, of the known reference event are compared with those of a generic ongoing event. If at any given moment they coincide or are similar, it can be assumed that for the aforementioned reasons, the expected damage will be comparable; otherwise, it will be different or attributable to another known critical reference event.
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