STUDIA UNIVERSITATIS BABEŞ-BOLYAI, GEOGRAPHIA, LIV, 2, 2009
G.I.S. MODEL FOR ACHIEVING THE SPATIAL CORRELATION BETWEEN AVERAGE MULTI-ANNUAL PRECIPITATIONS AND ALTITUDE ŞT. BILAŞCO1
ABSTRACT. – G.I.S. Model for Achieving the Spatial Correlation between Average Multi-annual Precipitations and Altitude. The model presents a work method for building a data content referring to the average multi-annual precipitations from a drainage basin, surveyed by few measurement stations with a view to achieving a hydric balance model with very good results. The existence of varied landforms imposes the identification of vertical gradients of the climatic element (average multi-annual precipitations) in relation to the altitude. For this reason, the regressions of the type: climatic element=f (altitude) have been studied. Keywords: modeling, database, spatial analysis, spatialization, G.I.S.
1.
THEORETICAL CONSIDERATIONS
In modern literature, hydrographic basin is seen as a hydrosystem whose inputs, drainage area (transit area) and outputs can be determined. Some of these components are known (precipitation, basin area), others can be identified as result of mathematical calculations and models (surface runoff, groundwater flow, evaporation). Atmospheric precipitations represent one of the main supply sources for the hydrographic basin, being also the climatic element with the greatest spatial and temporal variability, as far as duration, intensity, and frequency are concerned. The studied area, the Someşul Mic hydrographic basin, has a very small number of stations to measure the amount of precipitation, that is why, the development of some precipitation-runoff type models is impossible to achieve. The model presents a work algorithm for creating a database referring to the average multi-annual precipitation from a hydrographic basin, surveyed by few measurement stations, with a view to achieving, with very good results, a hydric balance model. The existence of a varied relief imposes the identification of the vertical gradients of the climatic element (average multi-annual precipitation) in relation to altitude. For this reason, the regressions of the type: climatic element = f (altitude) have been studied. In order to create the model, several stages must be passed through: the achievement of database (precipitation, numerical model of the terrain in DEM format), data validation, validity curve (regression models) selection and equation determination, the spatialization of the climatic element. 1
Romanian Academy, Cluj Subsidiary, Geography Section, 400015 Cluj-Napoca, Roumanie, e-mail:
[email protected]
ŞT. BILAŞCO
2.
DATABASE
The database referring to the average multi-annual precipitation was achieved by accessing bibliographic sources and by collecting data from the INMH for the stations: Vlădeasa 1800, Vlădeasa 1400, Stâna de Vale, Băişoara, Huedin, Beliş Lac, Căpuşu Mare, Gilău, Ştei, Câmpeni and Cluj (Tab 1, 2). The digital elevation model was created by using the contour lines with an equidistance of 40m as vectorial database, resulting a grid with a resolution of 20m. Amount of average multi-annual precipitation (according to Gaceu, O., 2005) Table 1 Name Vlădeasa 1800 Vlădeasa 1400 Stâna de Vale Băişoara Huedin Ştei Câmpeni
Altitude (m) 1836 1404 1108 1360 560 256 591
Precipitation (mm) 1151.3 1360.5 1570.7 847.4 596.7 681.0 738.0
Amount of average multi-annual precipitation (processed after the A.N.M. archive) Table 2 Name Beliş Lac Căpuşu Mare Gilău Cluj-Napoca
Altitude (m) 991 435 382 410
Precipitation (mm) 555.4 419.2 425.6 415.3
2. 1. Database validation At a first visual analysis regarding the representation of the amount of precipitation in relation to the altitude of the station they were measured at (Fig. 1), the existence of two distinct validity zones can be noticed. The existence of two validity zones I, II, leads to the determination of two different regression functions, valid for the territory found under the influence of the gauging stations the data were collected from. The passing from the scatteredly measured amounts of precipitation to their spatial estimation and therefore to the identification of the influence zone of each pluviometric station is achieved by using the Thiessen polygon method (Fig. 2).
72
G.I.S. Model FOR ACHIEVING THE SPATIAL CORRELATION
1800
I
PrecipitaŃii (mm)
1600 1400 1200 1000 800 600 400 200
II
0 0
500
1000
1500
2000
Altitudinea (m) Fig. 1. Validity zones.
This method assigns an influence zone to every pluviometer, whose area, estimated in percents, represents the weighting factor of the local value.
Fig. 2. Thiessen polygons and validity zones.
73
ŞT. BILAŞCO
As a result of Thiessen polygons, the two validity zones (Fig. 2) and the pluviometers taken into consideration for each were delimited, and, at the same time, the three pluviometers that did not influence the studied area were excluded (Tab. 3). 3. SPATIAL ANALYSIS Pluviometers/ validity zone, excluded pluviometers Table 3 Validity zone
Zone I
Pluviometer Stâna de Vale Huedin Căpuşu Mare Gilău Cluj Vlădeasa 1800 Băişoara Beliş Lac Ştei Câmpeni Vlădeasa 1400
The alphanumerical database, in grid format, was adapted according to the two validity zones, the grid being cut in conformity with the contour of each zone. Thus, two distinct grids resulted, each having the shape and the dimensions of the validity zone it belongs to (Fig. 3).
3. 1. Regression curve selection
Regression curves, as well as their equations, are created based on the data resulted from the pluviographs specific Excluded pluviometers to each validity zone. Regression curve defining is achieved by averages of the demo variant of the CurveFit programme. By regression function is averaget a mathematical expression, deduced as result of some experimental data processing, which approximates the dependencies between two or more variables of a system or process. The determination of a regression function is necessary when the dependencies between the respective variables cannot be established in a sufficiently accurate manner by theoretical averages. Once the value of pluviometers is known, a simple mathematical expression of a surface in the space with n+1 dimensions can be found, so that the surface can optimally approximate, after a certain criterion, the multitude of pluviometers. The mathematical expression will not coincide with the theoretical one, but it will approximate it in a sufficiently accurate manner so that it may allow its use in practical applications or even as initial hypothesis in some theoretical studies. The quality of approximation is deduced based on the standard error of estimation and on the correlation coefficient. Standard error characterizes the scattering of points around the graphic of the regression function, having a value as much closer to zero, as the respective points get closer to graphic. Correlation coefficient represents a measure of the rapport between the scattering degree of points around the graphic of the regression function and the scattering degree of the same points in rapport with the arithmetic average of the own ordinates. The value of this coefficient represents a more precise measure of the quality of the regression function obtained in the cases in which the standard deviation of values is relatively high. It is considered that the closer the value of the correlation coefficient is to the unit, the better a regression function approximates the set of experimental points. Zone II
74
G.I.S. Model FOR ACHIEVING THE SPATIAL CORRELATION
Fig. 3. Grid validity zones.
By using the CurveFit programme and by taking into account the values of the correlation coefficient and of the standard error (Tab. 4), the following functions were obtained: for the validity zone I, the Quadratic Fit regression function (Fig. 4) and for validity zone II, the Linear Fit regression function (Fig. 5).
Function validity indices Table 4 Function
Standard error
Correlation coefficient
CHI test
32.13 39.37
0.998 0.997
YES YES
Quadratic Fit Linear Fit
Quadratic Fit function
y = a + bx + cx 2
(1)
a = 6.05, b = 0.75, c = 0.00059, x – DEM, y – precipitation
75
ŞT. BILAŞCO
Fig. 4. Quadratic Fit function and afferent residuum.
Linear Fit function
y = a + bx
( 2)
a = -19.02, b = 0.62, x – DEM, y – precipitation
Fig. 5. Linear Fit function and afferent residuum.
3. 2. Spatialization of precipitation Once the regressions and equations are defined for each validity zone, it can be passed on to the spatialization of precipitation in relation to altitude. Spatialization is done by using the geoinformational programmes, such as ArcGis in our case. By appealing to the raster calculator module of the spatial analyst extension, the two equations were introduced, using as altitudinal base the digital elevation model, under the following form: validity zone I 6.05 + 0.75 * [Validity zone I] + Pow (0.00059 * [Validity zone I], 2) validity zone II - 19.02 + 0.62 * [Validity zone II], resulting a new database composed of two spatial entities in grid format, which have as numerical attributes the value of the average multi-annual precipitation on each separate pixel (Fig 6), (Fig. 7). 76
Fig. 8. Variation of average multi-annual precipitation in relation to altitude.
G.I.S. Model FOR ACHIEVING THE SPATIAL CORRELATION
77
ŞT. BILAŞCO
Fig. 6. Precipitation in validity zone I.
Fig. 7. Precipitation in validity zone II.
With a view to integrate the resulted database into spatial analysis models, it must be unitary (a single spatial entity over the entire analyzed area). Merge grid function was used in the process of creating the unitary grid (see Fig.8). The resulted database has a special importance, being used as input element in creating hydrologic balance models and models of achieving runoff storage on hydrographic basins.
REFERENCES
1. Clark, R. T., (1973), Mathematical models in hydrology, irrigation and drainage, Paper No. 19, FAO of the United Nation, Rome. 2. Haidu, I., (1997), Modele conceptuale şi stochastice de prognoză pe lungă durată a nivelurilor lacurilor. AplicaŃie lacul VârşolŃ. 3. Haidu, I., Chong-Yu Xu, (1999), Modelarea bilanŃului hidric al bazinului hidrografic la scară lunară, Studii şi cercetări de geografie. 4. Stănculescu, V. Al., (1985), Modele matematice în hidrologie, Institutul de meteorologie şi hidrologie, Bucureşti.
78
