Grid Arithmetic

The dialog Grid Arithmetics offers to generate new grids from several input grids, for example, in order to generate the sum or the difference of grids.

Dialog options

Use Grid

The current grid is assigned by R0 (or r0). By clicking on the file selector symbols up to 6 saved grids can be loaded (file formats *.cna or *.cnr).

Expression for new Grid

In these boxes a formula can be entered for each evaluation parameter defined using the grids R0 and R1 to R6 respecting the rules for expressions and operators (see Chapter 5 - Operators & Functions in the manual „Attributes, Variables and Keywords). When clicking OK the new grid is calculated processing the numerical expression/s.

Example:

grid R1 with obstacles and screening
grid R2 without obstacles
difference grid R2-R1 showing screening effect (A_bar) as a grid map

For further examples see the CadnaA-manual „Attributes, Variables, and Keywords“.

Double Arrow (>>)

gives access to pre-defined grid designations (based on grids R0 and R1, analogously for grids R2..R6).

Input Boxes for Evaluation Parameters

The check boxes in front of the four evaluation parameters enable to define specific expressions for each evaluation parameter. Per default, none of the check boxes is activated. This causes the expression for the first evaluation parameter (Ld/Day for evaluation parameter LP1, see Evaluation Parameters Tab) to be applied to all other evaluation parameters as well. Activate the respective check box to enter a different expression for this evaluation parameter.

New Grid is Intersection of Input Grids

When several grids are loaded this option causes to just evaluate and display the grid area which is an intersection of the input grids (i.e. where the input grids are overlapping). This option is activated by default.

Grids in Variants

Provided the project file contains several variants these can be assigned as well - besides the current variant (for table with variables, see Grid Variables for Evaluation Parameters).

Examples

Grid Summation

Enter in the first input box „Expression for New Grid“ the formula r0+1. Since the check-boxes for the other evaluation parameters are deactivated, the calculation is applied all evaluation parameters in the same way.

Note

The same effect would occur when activating all check-boxes and entering into each input box, starting from the first one: r01+1, r02+1, r03+1 and r04+1.

Energetic Summation

In this example, the current grid (r0) and the loaded grids R_B.CNA and RK_G.CNA are added energetically. From this sum the loaded grid RK_STR.CNA are linearly subtracted. By using the settings below the calculation occurs for all evaluation parameters using the same expression.

Difference Grid

In this example, the grid is calculated and saved using a point source in front of a reflecting barrier. Afterwards this file is loaded to field R1. Now, deactivate the reflection (by setting the reflection order to zero on tab „Reflection“ in the configuration, see Reflection Tab) and restart the grid calculation.

Calculate the difference by subtracting the current grid (r0) from the loaded grid R1 using the expression r1-r0. The resulting grid shows the level increase due to reflection.

Grid Variables for Evaluation Parameters

In a grid or a grid file up to four evaluation parameters plus a ground grid can be saved. The reference to a variant must be added with @Vy:

RxEvalParaNo@Vy

with x=0 .. 6, y=1 .. 16, EvalParaNo=1 .. 4

In case the designation for the variant @Vy is missing, the current variant is evaluated. The counting of the variant number y includes all defined variants, i.e. also those variants which may be temporarily deactivated.

The distinct grids can be addressed as follows:

R0	refers to the current grid with all defined evaluation parameters. A grid arithmetics would effect all grids of all evaluation parameters of the active variant.
R01 to R04	grid for evaluation parameters 1 to 4 of the active variant
R0g	refers to the current ground grid of the active variant
R1	refers to a saved grid loaded to input box R1 and effects the grids of all evaluation parameters Without a variant designation the first variant in a CadnaA file (.cna) is addressed. NOTE - In a CadnaA grid file (.cnr, saved via menu Grid\|Save as) at maximum four grids of the active variant are saved.
R11 to R14	refers to the grid loaded to input box R1, just for one the defined evaluation parameters 1 to 4 (regarding variants, see above)
R1g	refers to the ground grid loaded to input box R1
R3 to R6	analogously as before
R0@V1	refers the current grid of all evaluation parameters in variant V01
R01@V2 to R04@V2	refers the current grid of one of the evaluation parameters 1 to 4 in variant 2
R1@V1	refers the grid of all evaluation parameters in variant 1, loaded into input box R1
R11@V3 to R14@V3	refers the grid of one of the evaluation parameters 1 to 4 in variant 3 of a CadnaA file (*.cna), loaded in R1
R61@V16 to R64@V16	refers the grid of one of the evaluation parameters 1 to 4 in variant 16 of a CadnaA file (*.cna), loaded to input box R6

If the option „for all variants“ (dialog Grid|Properties) is deactivated, always the first variant is used.

Combining Grids using different Calculation Areas

When combining grids which are using different calculation areas, please note that CadnaA compresses all grids automatically upon calculation in order to save disk space. In these cases - especially when grid arithmetics is displaying odd results - it requires to decompress all grids prior to applying the grid arithmetics (see Receiver Grid).

Areas of designated Land Use

In addition to accessing levels via LP1...4, all attributes of the grid evaluation (see Grid Evaluation) can also be used to access, for example, limiting values of areas of designated land use.

Grid calculations for EU-noise indices with CRTN

When applying the English guideline CRTN ("Calculation of Road Traffic Noise") in conjunction with calculations according to the EC Environmental Noise Directive EU2002/49/EG-2002 the L₁₀ grid can be converted to a L_eq grid according to method 3 of the TRL-study (TRL-2002) in order to evaluate L_den and L_n.

The entire procedure requires several steps:

setup for calculation of initial levels L_A10,18h for Non-Motorways and Motorways: In order to calculate L_A10,18h select the performance parameters L_d on the tab Performance Parameters (Calculation| Configuration menu) with CRTN selected as road standard.

Later, the conversion of levels L_A10,18h into levels L_den and L_n according to TRL-study can be performed with both, non-motorways and motorways, in a single CadnaA-file provided that non-motorways and motorways are addressed to two variants.

Define three variants, for non-motorways, motorways, and for all roads.

Define groups according to IDs being different for non-motorways and motorways, for example:

As the grid is calculated just for the active variant the grids for non-motorways and motorways has to be calculated in two steps.

Select variant "non-motorways" and calculate grid. Save this grid via Grid menu, Save as (e.g. filename "non_motorways.cnr").
Switch to variant "motorways" and calculate grid.

Next, the two grids for L_A10,18h are converted into grids L_den and L_n.

Activate the END-performance parameters 1: L_den and 2: L_non the dialog Configuration (Calculation menu). Make sure that hours are allocated to the three daily periods D, E, N and penalties are entered.
Convert grids using the following expressions via the dialog Grid Arithmetic (on Grid menu) for „Expression or a new Grid“ with the syntax:

crtn\_X (LA10,18h\_nonmot, LA10,18h\_mot)

with the possible evaluation parameters X = (d, e, n, den)

At the first location within the brackets, the L₁₀ grid for "non-motorways" is referenced (e.g. LA10, 18 h_nonmot). At the second location, the L₁₀ grid for "motorways" is referenced (e.g. LA10, 18 h_mot). With the specifications as in a following illustration the grids for L_den and for L_n result in a single step.

In the example above, the present grid is for „motorways“ (R0) while the loaded grid R1 is the grid for „non-motorways“. The expressions to be entered are:

for Lden: crtn_den(r11,r01)

for Ln: crtn_n(r11,r01)

Note

Please consider that the first grid has to be always the grid for non-motorways and the second for motorways.

In this example, the result are grid for L_den (1st parameter) and L_n (2nd parameter). Select variant "all" to activate both types of roads.

Explanatory Remarks

The TRL-study TRL-2002 lists regression formulas to recalculate L_eq for the time periods Day, Evening, and Night based on statistical evaluations. When just having daily traffic counts available „Method 3“ of the TRL-study applies.

For non-motorway roads:

\(L_{day}=0.95*L_{A10,18h}+1.44dB\) (Equation 1)

\(L_{evening}=0.97*L_{A10,18h}-2.87dB\) (Equation 2)

\(L_{night}=0.90*L_{A10,18h}-3.77dB\) (Equation 3)

For motorway roads:

\(L_{day}=0.98*L_{A10,18h}+0.09dB\) (Equation 4)

\(L_{evening}=0.89*L_{A10,18h}+5.08dB\) (Equation 5)

\(L_{night}=0.87*L_{A10,18h}+4.24dB\) (Equation 6)

The above equations will be used in CadnaA when converting the grid for L_A10,18h into the resulting grids for L_den and L_n.

Additional features for grid conversion with CRTN

CadnaA offers additional commands for converting L_A10,18h into L_d and L_e. The general syntax is:

crtn_x (LA10,18h_nonmot, LA10,18h_mot) where x = (d, e, n, den)

LA10,18h_nonmot: grid for non-motorways

LA10,18h_mot: grid for motorways

This conversion respects the allocation of hours and the entered penalties.

Example 1

The expression:

crtn_den (r01, r11)

converts the parameter 1 for non-motorways in the current grid (r01) and the parameter 1 for motorways of loaded grid r1 (r11) into Lden-grid.

For evaluation the Lden-grid based on Leq-levels Ld, Le, and Ln the expression is:

Lden(day, evening, night)

This conversion respects the allocation of hours and the entered penalties as well.

Example 2

Having three grid for Ld, Le, Ln calculated the Lden-grid can be generated as the 4th grid by entering the following expression:

Lden(r01, r02, r03)

converts the parameter 1,2,3 of the current grid (r01, r02, r03) into Lden grid