GIS
Cvičení 10. Mapová algebra
Mapa potenciálních průměrných ročních teplot vzduchu
Sestrojte mapu potenciálních průměrných ročních teplot vzduchu na území ŠLP Krtiny.
Proč?
•    interpolace bodových měření do prostorově souvislých dat na základě předem daných fyzikálních zákonů za využití GIS (mapová algebra).
zdrojová data
digitální model terénu klimatologická data
3. Postup:
Z dat klimatologických stanic (poloha ve smyslu nadmořské výšky a teploty) zjistíme regresní závislost teploty na nadmořské výšce a touto rovnicí přepočítáme DMT. Dále z DMT zjistíme sklony a expozice reliéfu a pomocí rovnic klimatologických závislostí zpřesníme vypočtené teploty na základě reliéfu terénu (koeficient relativní ozářenosti).
Průměrná roční teplota vzduchu
1. Tuřany               241
2.  Pisárky               223
3.  Babice               460
4.  Bukovinka          524
5.  Blansko              287
6.  Kuřim                 291
7.  Olomučany        360
8.  Hády                  420
9.  Soběšice            398
10. Vranov               440
11.  Polanka              296
12.  Krtiny                 430
13.  Proklest              540
m n.m. m n.m. m n.m. m n.m. m n.m. m n.m. m n.m. m n.m. m n.m. m n.m. m n.m. m n.m. m n.m.
8,9 °C
8.5 °C
6.6 °( 6,4 °C
8.4 °C
8.0 °C 7,6 °C
7.5 °C 7,2 °C 6,9 °C 8,2 °C
7.1 °C 6,1 °C
T = T1 + T2 [°C]
T1... závislost teploty na nadmořské výšce T2... oprava teploty na sklon a expozici terénu
T1 =10,593-0,0082 *[DMT]
T2 = A*K - A
A = 4,4 + T1*0,133
K = koeficient relativní ozářenosti
sklon										
	K	|   (1)0°-5°   |	| (2)5°-10° |	|  (3) 10°-15°  |	|   (4) 15°-20°   |	| (5)20°-25° |	|  (6)25°-30°  |	|  (7)30°-40°  |	|  (8)40°-50°  |	
	1(1) J            I	|   1.05(04)   |	|   1.38(03)   |	|    1.17(06)    \	|    1.22(08)    \	|    1.26(31)  ]	|    1.31 (34)    \	|    1.34(35)    \	|    1.37(40)    \	
	| (2) JV, JZ     \	|   1.04(05)   |	|   1.10(02)   |	|    1.16(01)    \	|    1.20(07)    \	|    1.24(30)  ]	|    1.26(33)    \	|    1.28(32)    \	|    1.30(39)    \	
	I O) V, Z         I	|   1.02(09)   |	|   1.06(20)   |	|    1.09(21)    \	|    1.11(14)^	|    1.12(27)    \	|    1.12(26)    \	|    1.10(29)    \	|    1.07(38)    \	
	| (4) SV, SZ    \	|   1.00(10)   |	|   1.02(11)   |	|    1.01 (15)    \	|    1.00(17)   ]	|    0.99(22)   ]	|    0.97(24)    \	|    0.92(28)    \	|    0.84(36)    \	
	| (5) S             |	|   0.99(13)   |	|   1.00(12)   |	|    0.98(16)    \	|    0.96(18)    \	|   0.93(19)  ]	|    0.87(23)    \	|    0.81 (25)    \	|    0.75(37)    \	
expozice										
Klimatologická data
Výškopis SHP
Teplota Výška
XLS
TopoToRaster
DMT
GRID
______T=T1+T2	
	
T	<----------------
	
T2=A*K-A
Ta
GRID    Raster    GRID    Raster     GRID Calculator            Calculator
Rovnice pro T1
GRID Raster Calculator
T1=10.593-0.0082*DMT A = 4.4 + 0.133*T1    F
GRID
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GRID
Expozice_r
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BRID
ERID
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Tvorba digitálního modelu terénu
3
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- & Lavers B D  slp_poly
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B D  slp_vrs
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+ ^ Distance + S^ Extraction .+.■ íj^ Generalization + S^ Groundwater + ÍJ^ Hydrology - ^ Interpolation i.....^ IDW
■   Jfr Kriging : ■■ Jfr Natural Neighbor i ■ fr Spline
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+   £fc  I nr^l
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Input feature data
"B   G»
Feature Layer
Field
Type
^slp_vrs ^7slp_poly
VAL
Contour Boundary
+

öl
DP
Output surface raster | D:\GIS\ternpV3lp_drntlO
Output cell size [optional)
ID
Output extent [optional)
Y Maximum
X Minimum
-1141702.100000
X Maximum
-603319.737000 Y Minimum
-577990.352000
OK
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Output surface raster
Output surface raster dataset.
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Drawing -      k   C              I  D M   A H I
m Arial
"TJ |io J   b  i   u   A_t  * v z£ t «Lv
-589242.757 -115754S. 163 Unknown Units
Zjištění závislosti teploty na nadmořské výšce
Pomocí lineární regrese v MS Excel (vytvořením grafu a přidáním spojnice trendu) získáme regresní rovnici pro závislost teploty a nadmořské výšky.
Fyl Microsoft Ewcel - klimadata
Soubor     Úpravy     Zobrazit     V[ožit     Formát     Nástroje     Data     Okno     Nápověda
D
C1
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f* 241
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^   m
Z  - £1 I ÉB ©     * ! Arial
10
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A
B
K
M
10
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12
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_15_ _16_
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20_ 21 22_ 23_ 24
1
3
Brno-Tuřany
Brno-Pisárky
Babice
Bukovinka
Blansko
Kurím
Qlomučany
Hády
Soběšice
10 Vranov
11  Polanka
12  Krtiny
13 Proklest
241.0 223.0 460.0 524.0 287.0 291.0 360.0 420.0 396.0 440.0 296.0 430.0 540.0
8.9 8.5 6.6 6.4 8.4 8.0 7.6 7.5 7.2 6.9 8.2 7.1 6.1
10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0
0.0
y = 10.593-0.0082X
FT = 0.9524
100.0
200.0
300.0
400.0
500.0
600.0
u Raster Calculator
Layers:
-U*j
7         8         9
jJjliLil
1          2         3
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|T1= 10.593- (0.0082 * [DMT])|
Raster Calculator
Layers:
About Buildii
DMT T1
A=4.4+(0.133*[T1])
=        o      And		
		
>	>=	Or
		
<	<=	Xor
		
(	)	Not
-Arithmetic —	
Abs          Int	
	
Ceil	Float
	
Floor	IsNull
	
-Trigonometric—	
Sin        ASin	
	
Cos	ACos
	
Tan	ATan
	
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About Building Expressions
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p Logarithms EKp        Log
Exd2 I    Loa2
r Powers—i Sqrt
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>	>=	Or
		
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-Arithmetic— Abs         Int	
	
Ceil	Float
	IsNull
Floor	
	
-Trigonometric —	
Sin        ASin	
	
Cos	ACos
	
Tan	ATan
	
-Logarith	ms—
Exp        Log	
	
Exp2	Log2
	
Exp10	Log10
	
r Powers—i Sqrt
Sqr
Pow
T1 = 10.593 - (0.0082 * [DMT]) A = 4.4 + (0.133*[T1])
Výstupy nerespektují Current workspace!
Untitled - ArcMap - Arclnfo
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Low: 5.18301
Value I High: 8.83535
I Low: 5.8373
B 0  DMT
Value | High : 573.866
! Low: 214.286
Display | Source | Selection |
5*1
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-592751.695 -1159077.971 Unknown Units
Input raster		I tf| 1
DMT	T	
Output raster		
D:\SkJon		
Output measurement (optional)		
DEGREE	-	
3S9 i^Hn		
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4  15 20
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7 30 40
8 40 50
Sklon  R
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Reclassification
Old values
Output raster
D:\SkJon_R
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Unique
Add Entry
delete Entries
Precision.
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Input raster	
| Sklon	~3 a?
Reclass field	
| Value	d
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A
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	K	(1)0°-5°	(2)5°-10°	(3) 10°-15°	(4) 15°-20°	(5)20°-25°	(6)25°-30°	(7)30°-40°	(8)40°-50°	
	(1)J	1.05(04)	1.38(03)	1.17(06)	1.22(08)	1.26(31)	1.31(34)	1.34(35)	1.37(40)	
	(2) JV, JZ	1.04(05)	1.10(02)	1.16(01)	1.20(07)	1.24(30)	1.26(33)	1.28(32)	1.30(39)	
	(3) V, Z	1.02(09)	1.06(20)	1.09(21)	1.11 (14)	1.12(27)	1.12(26)	1.10(29)	1.07(38)	
	(4) SV, SZ	1.00(10)	1.02(11)	1.01(15)	1.00(17)	0.99 (22)	0.97 (24)	0.92 (28)	0.84 (36)	
	(5) S	0.99(13)	1.00(12)	0.98(16)	0.96(18)	0.93(19)	0.87 (23)	0.81 (25)	0.75 (37)	
										
Reclassify   Expozice
sz 337.5;
'270°
,180°
202.5
1  157.5 202.5
2  112.5 157.5
2 202.5 247.5
3 67.5 112.5
3 247.5 292.5
4 22.5 67.5
4 292.5 337.5
5 0 22.5
5 337.5 360
Expozice_R
| S* Reclassify							^jnjxj	
Input raster								*. |
I	Expozice						zl tf|	
	teclass field							
F								
I	Value						zl	
Reclassification								
\	|          Old values          |	New values         IP		m				
				Classify...				
	J                 0-22.5	5	_ Z.					
	J              22.5-67.5	4						
				Unique				
	J             67.5 -112.5	3						
	J            í í 2.5-157.5	2						
	J             157.5-202.5	1		Add Entry				
	J             202.5-247.5	2						
	J             247.5-292.5	3		Delete Entries				
	I             292.5-337.5	4		I------------------------------'				
	Load...   I     5ave...							
		Reverse New Values I      Precision...						
								
Output raster								
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| D:\Expozice_R							e£	d
^^^^M							______IjJ	
								
		OK                  C	anc	el          Environments...			Show Help»   |	
								
Reklasifikované expozice svahů pro koeficient rel. ozářenosti
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1	1	0	•
	1	2	1 2
4		0	'
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1 VAUUE	COUNT	CODE
J      0 4	5 5 3 2	002 004 005 O03
VALUE	COUWT	TYPE
0 1      1 3	5 4 3 3	PAX HAB WIN SAN
VALUE=NOOATA
									
	VALUE	COUNT	1 NO Kl Dl	INGRIDS	X__	1	2	3	------------1 4
	1 S 3 4 7 7 e B	2 S 1 3 1 1 2 1 1	1 1 0 0 1 2 2 4 0	0 1 1 0 3 1 2 3 2					
							5	e	T
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						8	B	2	1
									
Expression; COMBINE(INÔHID1t INGRID2)							CHJTGRID		
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EXPOZICE  R
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Name: Type:
K | Float
31
Field Properties
Precision	6
[Scale______________	2
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SI
► | h|         Show: | All     Selected |        Records (0 out of 40 Selected)
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|  Drawing T      (fc   (	D *	A "	E	\;Ó] Arial	_^J |10   _3J    B   /    U	A~	<& -	.ä *   • ~		
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Adds a new field to the table									~ 1-593006.157 -1159124.925 Meters	
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K	(1)0°-5°	(2)5°-10°	(3) 10°-15°	(4) 15°-20°	(5)20°-25°	(6)25°-30°	(7)30°-40°	(8)40°-50°  |
1(1) J	1.05(04)	1.38(03)	1.17(06)	1.22(08)	1.26(31)	1.31(34)	1.34(35)	1.37(40)    |
| (2) JV, JZ	1.04(05)	1.10(02)	1.16(01)	1.20(07)	1.24(30)	1.26(33)	1.28(32)	1.30(39)    |
I O) V, Z	1.02(09)	1.06(20)	1.09(21)	1.11 (14)	1.12(27)	1.12(26)	1.10(29)	1.07(38)    |
| (4) SV, SZ	1.00(10)	1.02(11)	1.01(15)	1.00(17)	0.99 (22)	0.97 (24)	0.92 (28)	0.84 (36)    |
| (5) S	0.99(13)	1.00(12)	0.98(16)	0.96(18)	0.93(19)	0.87 (23)	0.81 (25)	0.75 (37)    |
	K	(1)0°- 5°	(2)5°-10°  |			(3) 10°-15°		|   (4) 15°-20°   |		(5)20°-25°  |		(6)25°-30°	(7)30°-40°	(8)40°-50°
	(1)J	1.05(04)	A   OQ  /n_~*      '			------é—a —f   tr\r\\-----		J-------é—CLO—tr\r\\-------L		-----é—ö-ö—tr\ a \------1—,		| 1.31 (34)	1.34(35)	1.37(40)
			1.00 (U		j Ŕowi<í		VALUEJ	COUNT	ASPECT_R	SLOPE_R2	K    j			
	(2) JV, JZ	1.04(05)	1.10 (o|	—		0	1	67024	2	3	1.16	1.26(33)	1.28(32)	1.30(39)
						1	2	123691	2	2	1.1			
	(3) V, Z	1.02(09)	1.06 (2|		2		3	64435	1	2	1.38	1.12(26)	1.10(29)	1.07(38)
					3		4	67451	1	1	1.05			
	(4) SV, SZ	1.00(10)	1.02(1		4		5	125566	2	1	1.04	0.97 (24)	0.92 (28)	0.84 (36)
					5		6	31752	1	3	1.17			
	(5) S	0.99(13)	1.00(1		6		7	41230	2	4	1.2	0.87 (23)	0.81 (25)	0.75 (37)
					7		8	19533	1	4	1.22			
					3		9	94652	3	1	1.02			
					9		10	86907	4	1	1			
					10		11	99278	4	2	1.02			
					11		12	47861	5	2	1			
					12		13	36983	5	1	0.99			
					13		14	34515	3	4	1.11			
					14		15	69078	4	3	1.01			
					15		16	33385	5	3	0.98			
					16		17	44002	4	4	1			
					17		18	20749	5	4	0.96			
					13		19	14089	5	5	0.93			
					19		20	104875	3	2	1.06			
					20		21	60369	3	3	1.09			
					21		22	28025	4	5	0.99			
					22		23	9211	5	6	0.87			
					23		24	16668	4	6	0.97			
					24		25	5579	5	7	0.81			
					25		26	13539	3	6	1.12			
					26		27	23273	3	5	1.12			
					27		28	10923	4	7	0.92			
					23		29	8753	3	7	1.1			
					29		30	26556	2	5	1.24			
					30		31	12301	1	5	1.26			
					31		32	6539	2	7	1.28			
					32		33	14027	2	6	1.26			
					33		34	6800	1	6	1.31			
					34		35	2341	1	7	1.34			
					35		36	216	4	8	0.34			
					36		37	85	5	8	0.75			
					37		38	223	3	8	1.07			
					33		39	95	2	8	1.3			
						39	40	28	1	8	1.37 j			
														
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Layera:
ex_skl
expozice_r
k
sklon_r
slp_aspect
slp_drnt10
slp_slope
T1
T?

T2=[A]*[K]-[A]
.About Building Expressions
Evaluatl
Layera:
ex_skl
expozice_r
k
sklonj-
slp_aspect
slp_dmt1D
slp_slope
T1
o      And
T=[T1] + [T2]
Or
Xor
m

7         8         9 4         5         6
1         2   I     3   I
0
j^bout Building Expressions
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JiJ1
o      And
>        >=       Or
<        <=      Xor
(          )        Not 1
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j^j
T2 = [A] * [K] - [A] T = [T1] + [T2]
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