Introduction
Methodology
-
identification of topographic conditions accompanying precipitation and building a spatial data model,
-
grouping of measurement stations with taking into account average precipitations,
-
develop a dependency model based on the relationship between the characteristics of the terrain and the class of precipitation.
Topographic conditions to separate regions
Spatial data model
-
measurement stations,
-
altitude - DTM,
-
declines of the terrain,
-
directions of terrain slope (exhibition),
-
land cover (land use),
-
physiogeographic unit,
-
river catchment areas.
Layers | Data format | Geometry | Resolution | Data type |
---|---|---|---|---|
Measurement stations | Vector | Point | - | Quantitative |
NMT | GRID | Elementary field in the form of square | 1 × 1 km | Quantitative |
Terrain slopes | GRID | Elementary field in the form of square | 1 × 1 km | Quantitative |
Directions of terrain slopes | GRID | Elementary field in the form of square | 1 × 1 km | Qualitative |
Land cover | Vector | Area | - | Qualitative |
Physio-geographic units | Vector | Area | - | Qualitative |
River catchments | Vector | Area | - | Qualitative |
Integrative layer TEMKART | GRID | Elementary field in the form of square | 1 × 1 km | Quantitative and qualitative |
Grouping stations
Applying artificial neural networks to the classification
-
\(I_{j}\) - input value,
-
\(O_{j}\) - output value.
Specification of test area
-
460 stations from 1881–1930,
-
250 stations from 1948–1980,
-
45 stations from 1981–2013.
Results
Grouping precipitation stations into classes according to average values of precipitation
-
average precipitation during the growing season from April to September,
-
average precipitation between May and June,
-
average precipitation between July and August and
-
average precipitation in July.
No. | IV–IX (mm) | V–VI (mm) | VII–VIII (mm) | VII (mm) | H a.s.l. (m) | Number of stations | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | ||
GI-1 | 303 | 345 | 95 | 122 | 124 | 142 | 68 | 80 | 28 | 146 | 44 |
GI-2 | 338 | 380 | 111 | 132 | 132 | 158 | 67 | 88 | 45 | 195 | 78 |
GI-3 | 352 | 405 | 117 | 144 | 139 | 167 | 79 | 95 | 62 | 373 | 42 |
GI-4 | 390 | 445 | 136 | 161 | 156 | 180 | 82 | 100 | 82 | 604 | 79 |
GI-5 | 426 | 485 | 145 | 175 | 171 | 196 | 93 | 112 | 172 | 670 | 60 |
GI-6 | 458 | 516 | 156 | 183 | 183 | 216 | 97 | 124 | 190 | 780 | 52 |
GI-7 | 519 | 634 | 177 | 223 | 200 | 242 | 107 | 135 | 296 | 800 | 33 |
GI-8 | 575 | 741 | 192 | 247 | 231 | 294 | 121 | 160 | 280 | 1603 | 29 |
GI-9 | 728 | 830 | 251 | 280 | 282 | 365 | 155 | 204 | 416 | 1490 | 10 |
No. | IV–IX (mm) | V–VI (mm) | VII–VIII (mm) | VII (mm) | H a.s.l. (m) | Number of stations | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | ||
GII-1 | 303 | 346 | 95 | 122 | 124 | 143 | 68 | 84 | 28 | 146 | 47 |
GII-2 | 338 | 373 | 113 | 144 | 132 | 152 | 67 | 87 | 45 | 186 | 65 |
GII-3 | 359 | 413 | 117 | 146 | 147 | 167 | 79 | 96 | 85 | 240 | 72 |
GII-4 | 389 | 455 | 135 | 154 | 157 | 182 | 89 | 104 | 335 | 470 | 18 |
GII-5 | 399 | 461 | 141 | 162 | 158 | 189 | 82 | 109 | 172 | 320 | 67 |
GII-6 | 430 | 500 | 136 | 175 | 161 | 209 | 89 | 112 | 380 | 780 | 18 |
GII-7 | 451 | 528 | 154 | 189 | 171 | 218 | 93 | 124 | 190 | 565 | 81 |
GII-8 | 522 | 631 | 177 | 215 | 200 | 248 | 109 | 136 | 280 | 800 | 37 |
GII-9 | 575 | 830 | 196 | 280 | 231 | 365 | 128 | 204 | 300 | 1603 | 31 |
Applying artificial neural networks to the classification of areas according to chosen conditions accompanying precipitation
-
an elementary field cannot be further than 3.5 km from a measurement station,
-
an elementary field should be located in the same physiographic unit as the precipitation measurement station,
-
an elementary field belongs to the same catchment as the precipitation measurement station.
Option I—without taking altitude into account during multi-criteria classification of patterns
Class | Number of patterns | Percentage (%) | Number of stations in the class | Percentage (%) |
---|---|---|---|---|
GI-1 | 306 | 5.1 | 9 | 3.8 |
GI-2 | 1374 | 22.9 | 40 | 16.7 |
GI-3 | 795 | 13.2 | 24 | 10.0 |
GI-4 | 1432 | 23.9 | 55 | 22.9 |
GI-5 | 663 | 11.1 | 36 | 15.0 |
GI-6 | 586 | 9.8 | 28 | 11.6 |
GI-7 | 475 | 7.9 | 25 | 10.4 |
GI-8 | 285 | 4.8 | 17 | 7.1 |
GI-9 | 79 | 1.3 | 6 | 2.5 |
\(\Sigma\)= 5995 | \(\Sigma\) =100% | \(\Sigma\) =240 | \(\Sigma\) =100% |
Option II—taking into account altitude during multi-criteria classification of patterns
Class | Number of patterns | Percentage (%) | Number of stations in the class | Percentage (%) |
---|---|---|---|---|
GII-1 | 385 | 6.4 | 11 | 4.6 |
GII-2 | 1047 | 17.3 | 31 | 12.9 |
GII-3 | 1455 | 24.1 | 43 | 17.9 |
GII-4 | 349 | 5.8 | 16 | 6.7 |
GII-5 | 878 | 14.5 | 33 | 13.8 |
GII-6 | 209 | 3.5 | 10 | 4.2 |
GII-7 | 959 | 15.9 | 49 | 20.4 |
GII-8 | 501 | 8.3 | 27 | 11.2 |
GII-9 | 256 | 4.2 | 20 | 8.3 |
\(\Sigma\)=6039 | \(\Sigma\)=100% | \(\Sigma\)=240 | \(\Sigma\)=100% |
Classification of elementary fields
-
If one neuron on the output layer gives \(p1 \ge 0.7\), option I is fulfilled and the case is considered as certainly belonging to the class represented by the neuron
-
If one neuron on the output layer gives \(p1 < 0.7\) and \(p1\ge 0.5\), then option II is fulfilled. If the activation value of the next output neuron is 2.5 times less than p1, then the case is also considered as certainly belonging to the class represented by the neuron.
-
If one neuron on the output layer gives \(p1 < 0.7\) and \(p1\ge 0.5\) and a \(\frac{p2}{p3} < 2.5\) appears, the alternative class 1 can be indicated if the condition III, \(\frac{p2}{p3}\ge 2.5\), is met. In practice, it means that the probability of indicating the correct class is more than or equal to 0.5. However, the second neuron also obtains a relatively high value less than 0.5, while the third one, when it comes to value, which represents the class, obtains a significantly different probability from the second neuron; thus, the alternative class 1 can be distinguished.
-
If the relationship \(\frac{p2}{p3}<2.5\), then the differences between output values are so small that it is difficult to indicate one alternative class.
Criterion I | Criterion II | Criterion III | Classification characteristics | Description on the map |
---|---|---|---|---|
\(p1 \ge 0.7\)
| – | – | Choice of one class.Certain selection of the base class | Dependable |
\(0.5\le p1<0.7\)
|
\(\frac{p1}{p2}\ge 2.5\)
| – | Choice of one class.Certain selection of the base class | Dependable |
\(0.5\le p1 < 0.7\)
|
\(\frac{p1}{P2} <2.5\)
|
\(\frac{p2}{p3}\ge 2.5\)
| Choice of less certain base class and the choice of alternative class. The probability of belonging to the other class determined by p2 is relatively high | Dispensable |
\(0.5\le p1 < 0.7\)
|
\(\frac{p1}{P2} <2.5\)
|
\(\frac{p2}{p3}<2.5\)
| Choice of less certain base class lack of alternative class.The probability of belonging to the other class determined by p2 and p3 is relatively high. Lack of belonging to one alternative class | Less reliable |
\(p1 < 0.5\)
| – | – | Lack of possibility to choose base class. Uncertain belonging | Unreliable |
Discussion
Conclusion
-
spatial analysis of phenomenon distribution in relation to topographic factors accompanying the studied phenomenon without determining the mathematical function of the relationship between them,
-
spatial analysis of phenomenon distribution taking into account attributive data describing factors accompanying the studied phenomenon,
-
indicating borders of phenomenon’s spread and transitional zones on the basis of point measurements,
-
indicating areas without patterns, that is, measurement stations in the areas with features not similar to classified areas.