Rocchi

Maria Ioannilli and Enrico Rocchi

University of Rome “Tor Vergata”

“Urban Roughness Parameters Calculation in the City of Rome by Applying Analytical and Simplified

Formulations: Comparison of Results”

The International Conference on Computational Science and ApplicationsPerugia 2008

Geographical Analysis, Urban Modelling, Spatial Statistics

The presentation of the work is divided into the following steps:

Urban Canopy Parametrization (UCP) Urban Canopy Parametrization (UCP)

General assumption for parameters calculationGeneral assumption for parameters calculation

ImplementationImplementation

ResultsResults

This work has the aim to analytically determine some of the UCP parameters and an automatic procedure has been implemented by Arcgis 9, by using as input data the vectorial numerical geodatabase of the city of Rome, coded in 1:2.000 scale.This procedure has been applied to the IX district of Rome, whose full extent is about 8.1 km2.

MESOSCALE METEREOLOGICAL MODELS

“URBAN CANOPY PARAMETRIZATION” (UCP)

Urban Canopy Parametrization (UCP)

URBAN CANOPY PARAMETERIZATION

The geometric and morphological characteristics of the urban installation are represented through the set of parameters below

Canopy UCPs Building UCPs Vegetation, Other UCPs

Mean canopy height

Canopy plan area density

Canopy top area density

Canopy frontal area density

Roughness length

Displacement height

Sky view factor

Mean building height

Standard deviation of building

height

Building height histograms

Building wall-to-plan area ratio

Building height-to-width ratio

Building plan area density

Building rooftop area density

Building frontal area density

Mean vegetation height

Vegetation plan area density

Vegetation top area density

Vegetation frontal area density

Mean orientation of streets

Plan area fraction surface covers

Percent directly connected impervious area

Building material fraction

Canopy UCPs Building UCPs Vegetation, Other UCPs

Mean canopy height

Canopy plan area density

Canopy top area density

Canopy frontal area density

Roughness length

Displacement height

Sky view factor

Mean building height

Standard deviation of building

height

Building height histograms

Building wall-to-plan area ratio

Building height-to-width ratio

Building plan area density

Building rooftop area density

Building frontal area density

Mean vegetation height

Vegetation plan area density

Vegetation top area density

Vegetation frontal area density

Mean orientation of streets

Plan area fraction surface covers

Percent directly connected impervious area

Building material fraction


These two parameters express the change of the aerodynamic characteristics of the territory caused by the cityThe city, in fact, is characterized by a so called urban roughness, which is the cause of the wind velocity decrease, and of turbulence and energy’s exchanges increase.

The following pictures show three examples of different degrees of urban roughness : high (a), middle (b) and low (c)

(a) (b) (c)

Urban Canopy Parametrization (UCP) - Roughness length (Z0) and Displacement height (Zd)


For the aim of the work, the roughness length and the displacement height have been selected among the range of the UCP parameters.

The Planetary Boundary layer (PBL), near the urban installation, is called URBAN BOUNDARY LAYER (UBL) The lower part, called SURFACE LAYER, can be divided into:

ROUGHNESS SUB-LAYER (RSL) it is the layer in contact with the terrestrial

surface in which the flow fields are influenced by the characteristics of the single urban structures the so called “ roughness elements” contains:

URBAN CANOPY LAYER (UCL) it is the layer included among the

ground and the roofs of the buildings in which the atmospherical properties are strongly influenced by the human activities. The height of the RSL is around 2-5 times the height of the UCL

INERTIAL SUB-LAYER (ISL)



( )0

ln du z zU z

zk*

æ ö- ÷ç ÷ç= ÷ç ÷÷çè ø

where: U(z) is the wind average velocity Z is the height above the ground Z0 is the “roughness length”

Zd is the “displacement height”

u* is the friction velocity K is the Von Kármán constant , equal to 0.4

DISPLACEMENT HEIGHT (Zd)When the roughness elements are near, the flow is lifted above them with a value equal to Zd



INERTIAL SUB-LAYER (ISL) This layer doesn’t feel the effects of the single roughness elements, and the aerodynamic characteristics of the city are represented by only a parameter, the “ROUGHNESS LENGTH” (Z0). In this layer the wind velocity has a logarithmic profile which changes with the altitude, as the following expression:

Raupach’s model (1994)

Bottema’s model (1997)

Urban Canopy Parametrization (UPC) Urban Canopy Parametrization (UPC)

Roughness length (Z0) and Displacement height (Zd): calculation models


For the aim of the work, two methods and an experimental application have been used.

Bottema-Mestayer’ application (1998)

The models study the “MUTUAL SHELTERING” problem in a different way.(the mutual sheltering is a relative decrement of the wind velocity caused by an obstacle towards another).

Raupach’s model it studies the problem through the introduction of a shelter coefficient C which follows from the ratio w/h

Bottema’s model it studies the problem using the Zd as parameter of mutual sheltering, founding itself on the calculation of the distances dx and dy among the obstacles

Raupach’s model (1994) has been developed for random building arrangements. Raupach introduces these two equations that tie the aerodynamic parameters to the middle height of the buildings and to the frontal area index

1

1

1 exp( 2 )1

2Fd

F

cz

h c

l

l

- -- =

0*

( )exp( )exp hd k

Uz h z k

u

æ ö÷ç ÷= - - Y -ç ÷ç ÷çè ø

*

*

exp2

12

hF

h

S dh F

Uc

uU

uC C

l

l

æ ö÷ç ÷ç ÷ç ÷çè ø=

+

Raupach’s model can be used for frontal area densities lower than 0.1–0.2 because the model cannot describe overlapping of sheltering in dense arrays.

Increasing the involved frontal area, the effect of mutual sheltering becomes more meaningfulI and the evaluation of Zo can be overestimated

Raupach’s model (1994)


Roughness length (Z0) and Displacement height (Zd) : calculation models

Zo and Zd are linked to the logarithmic wind profile: *

0

( ) ln du z zU z

k z

æ ö- ÷ç ÷= ç ÷ç ÷çè øThe basic model equation used is :

0 ( ) exp0.5 ( , , / ,....)

ref d

F d ref F

kz z z

C z w hl l

æ ö÷ç ÷ç= - - ÷ç ÷ç ÷÷çè øWhere:Zref = reference height Cd = drag coefficient

Fx y

wh

d dl =Frontal area density:

xP

x y

wl

d dl =

A common alternative approach is :• choose a reference level Zref = h • use Zd as a mutual sheltering parameter

Plan area density:

Bottema’s model (1997)

Zo :0 ( ) exp

0.5d

F dh

kz h z

Cl

æ ö÷ç ÷ç= - - ÷ç ÷ç ÷è ø



They are assumed to have triangular x – z cross section, and their width is assumed to be equal to the buildings width w. In this way, the recirculation volume is approximated as:

RECIRCULATION ZONE

where LR and LF are the frontal and leeward recirculation zone lengths

( )3R F

whL L+

LR and LF are estimated from numerical and experimental results. They are approximated as LR + LF = 4Lg

where Lg is the geometrical influence scale: 2

2g

whL

h w=

+



Mutual sheltering in regular arrangements with large lateral spacings (say Sy/w >1) may not be well described by an average upward flow displacement zd . Hence, an “in-plane” zero displacement height zd,pl is used instead of zd; for zd,pl , only the buildings rows are considered, not the streets parallel to the wind in between.

In normal arrays zd and zd,pl are related by: zd = (w / dy) zd,pl

The calculation of zd,pl is a function of : dimension of the recirculation zone, density and arrangement of the obstacles 4Lg+lx

lx

h2h/3

STAGGERED ARRAYS WITH OVERLAPPING ROWS (w > dy)

, , ( ) , ( )

2 21 2d d pl d pl staggered d pl normal

dy dyz z z z

w w

æ ö æ ö÷ ÷ç ç= = - + -÷ ÷ç ç÷ ÷ç çè ø è ø dy / w < 1

NORMAL ARRAYS

,43g

xd pl

x

Llz

h d

+=

,

24 3

x xx

gd pl

x

S Sl

Lz

h d

æ ö÷ç ÷ç+ - ÷ç ÷÷çè ø=

for low densities, if: Sx > 4Lg

for high densities, if: 4Sx Lg£

STAGGERED ARRAYS

,

43

2

xd pl

Lglz

dxh

+= for low densities, if : 4

2x

x g

dS L- >

,

2 224 3

2

x

d pl

dx dxSx Sx

lLg

z

dxh

- -+ -

=

æ öæ ö÷ ÷ç ç÷ ÷ç ç÷ ÷ç ç÷ ÷ç ç÷ ÷ç ç÷ ÷÷ ÷ç ç÷ ÷ç ç÷ ÷ç çè øè ø for high densities, if : 42x

x g

dS L- £



Because of measuring problems related to evaluation of urban roughness parameters, a new approach using a roughness mapping tool has been tested: evaluation of roughness length Zo and zero displacement Zd from cadastral databases which contains all buildings within a 2.7 x 2.2 km2 area in the centre of Strasbourg

The basic model of the present application, for the calculation of roughness length is Bottema’s model (1997).

The main difference between this application and the basic model is the evaluation of the zerodisplacement height Zd. For irregular groups, a direct calculation of Zd from the volume of buildings and their recirculation zones is far too complicated. Therefore, a simple power-law approximation of regular-group-model results is used:

( )0.6( )d Pz h l=

Assumed wind direction: N or S


The ordinary application

In this equation Zd is a function of plan area density

Bottema-Mestayer’ application (1998)

BASIC MODEL

Bottema’s model has been taken as reference and it has been adapted to the analyzed urban environment.

to analytically estimate the main parameters: h, 4Lg, dx, lx, Sx, dy, w, Sy

OBJECTIVE

to estimate the plan and frontal area density

to calculate zd,pl and z0 according to the Bottema's canonical formulation

Realization of an automatic procedure of calculation which, departing from the description of a urban context, allows :

to choose the wind direction for which we estimate the main parameters


Work’s objective

Realization of an automatic procedure of calculation that allows to apply the Bottema’s formulation to the urban contexts

to create a reference database

to calculate zd,pl and z0 according to the Bottema-Mestayer’s formula and Raupach’s method

to make a comparison between the three methods

we establish the arc’s orientation through the evaluation of the angle alfa

Eight possible cases are evaluated:

To be able to identify the fronts of the blocks that have involved from any wind direction, it is necessary to estimate their absolute orientation

Every front must be qualified according to its inclination (radiant) in comparison to a direction taken for reference (north–south)

In this way: every front must be represented as an arc with an initial and final node for each arc we consider the length L and the coordinates of the final node P2 = (X2,Y2) and of the

initial node P1 = (X1,Y1) we calculate the distance B and A and the angle:

arcsinB

La

æ ö÷ç= ÷ç ÷çè ø

General assumptions for the calculation of the parametersGeneral assumptions for the calculation of the parameters

1 – Qualification of the blocks’ fronts in relation to the wind direction

(4)General assumptions for the calculation of the parametersGeneral assumptions for the calculation of the parameters

1 – Qualification of the block's fronts relatively to the wind direction

HEIGHT h The height of the building block is evaluated through an average weighed on the area of the

heights of the different building units which compose it Each arc, which represents a front of the block, must be characterized by the height of the block

to which it belongs

1

,

n

i ii

arctot block

h Ah

A==å

RECIRCULATION VOLUME (4Lg)

2

2g

whL

h w=

+


2 – Analytical evaluation of the main parameters

dx, lx, Sx The value of dx is calculated tracing, from

the middle point of every analyzed arc, a parallel straight line to the wind direction in order to estimate the distance dx from the fronts of the intersected blocks

As the blocks • don't have regular shape and • the wind direction can vary

we suppose that the length lx is equal to the part of the straight line contained in the analyzed block


2 - Analytical evaluation of the main parameters

Sx = dx - lx

The dy must be analytically valued according to the geometry of the involved building’s blocks

The characteristic point of the overlooking block (P1 or P2), that allows to evaluate L is located considering the direction and the orientation of the analyzed arc. According to these two parameters the point of the block (frontally arranged) is chosen with coordinate Y or X great or small



dy, w, Sy



dy, w, Sy

dy, w, Sy



To recognize the building blocks frontally arranged (according to the wind direction ) to the considered arc, we trace the parallel straight lines to the wind direction which have as starting point respectively the initial, middle and final point of the analyzed arc

When more building’s blocks overlooking the analyzed arc are individualized, and therefore there are more values of dy, an only value is calculated as followed:

i idy wdy

w=å

Basic unit for the calculation of the parameters: 100 x 100m spatial 2-D grid. The grid can run according to any direction.

Zd

Zo

Zd :

Evaluation of a single arc involved in the chosen wind direction :

Evaluation for a single cell :

( )1

1

n

d i ii

d n

ii

z Lz

L

=

=

×=å

å

0( )1

0

1

n

i ii

n

ii

z Lz

L

=

=

×=å

å

Bottema’s model

Plan area density λP

Frontal area density λF

1i

n

Pi

Prugoxel

A

Al ==

å

Zo :1

i

n

Fi

Frugoxel

A

Al ==

å


3 – Evaluation of: λp λf Zd and Z0

Vectorial numerical cartography of Rome, encoded to scale 1:2000, produced by Cartesia SpA

Class Built area Group Volumetric unit

polygonals of volumetric units encoded to:• volumetric unit identification• area• perimeter• Rooftop height• height

Used data


IX municipality: database

n. road arcs 1593

n. building blocks 503

n. volumetric units 10453

Studied area


IX municipality It contains part of the districts:

Tuscolano, Appio Latino e Prenestino Labicano

It connects the historical center to the suburb. It has an area of 8.1 km2 and a population of 134.078 inhabitants.

It’s limited to east from the railroad and to west from the Park of the Caffarella, it is crossed by important streets as the Tuscolana and the Appia Nuova and in the middle of it there is Re di Roma square.

Moreover, it is characterized by a consistent archaeological and naturalistic patrimony, which develops along the road axle of the Latina Street and the Appia Antica.

Tools: software GIS ARC/Info


Because of the strong territorial character of the studied problem, the GIS software has been chosen as an effective tool of resolution, particularly in the optics to develop an automatic procedure of calculation valid for every urban context

We have chosen, therefore, to use the software ArcInfo, with all its extensions

We have elaborated a AML script (ARC/Info Macro Language) to implement the automatic procedure of calculation on the Municipio IX

STEP 1 : development of basic cover

STEP 2 : calculation of geometric parameters and development of the reference final file

STEP 3 : main evaluation parameters

BUILDINGS

BUILDING BLOCKS IDENTIFICATION

ROAD NETWORK

CHOICE OF THE WIND DIRECTION

DETERMINATION OF THE INVOLVED ARCS

REFERENCE FINAL FILE

BASIC COVER

PARTICULARITYEVALUATION

STEP 2: CALCULATION OF GEOMETRIC PARAMETERS AND DEVELOPMENT OF THE REFERENCE FINAL FILE

General elaboration flow


STEP 1: DEVELOPMENT OF BASIC COVER

IDENTIFICATION OF THE INSIDE BLOCKS TO THE ROAD NETWORK

DETERMINATION OF THE ARCS ORIENTATION OF THE BLOCKS

DEFINITION OF THE BLOCKS SIDES

BASIC COVER

GEOMETRIC PARAMETERS CALCULATION

REFERENCE FINAL FILE GRID 2-D OVERLAP

CALCULATION OF λf, λp AND h FOR EVERY GRID CELL

CALCULATION OF Zo AND Zd,pl FOR EVERY GRID CELL

CALCULATION OF Zd,pl AND Zo WITHBOTTEMA-MESTAYER’S APPLICATION

FINAL RESULTS FILE

STEP 3: MAIN EVALUATION PARAMETERS

CALCULATION OF Zd,pl AND Zo WITHRAUPACH’S MODEL

STEP 1 : development of basic cover


1 2

3 4

1 - input (polygonal volumetric units)2 - elaboration (urban blocks polygonal)3 - elaboration (linear blocks topology)4 - elaboration (single fronts identification)

Choice of the wind direction

Selection of the involved arcs : 694 su 1431

N

340°

N

140°





middle points dx

dy

STEP 3 : main parameters evaluation

Zd

Zo

Zd and Zo Raupach’s model:

1

1

1 exp( 2 )1

2Fd

F

cz

h c

l

l

- -- = 0

*

( ) exp( )exp hd k

Uz h z k

u

æ ö÷ç ÷= - - Y -ç ÷ç ÷çè ø

( )0.6, ( )d pl pZ h l=

Plan area density

Frontal area density

Zd and Zo Bottema-Mestayer’s application:


ResultsResults

To evaluate the obtained results, the following operations have been performed :

1. comparison with the obtained results by the application of Bottema-Mestayer's method and Roupach's model to the studied area

2. verification of the Zd and Zo parameters, calculated with the three methods, in relation to the plan and frontal area density

3. comparison with the obtained results implementing again the procedure of calculation, modifying the choice of the wind direction . This allows to underline the addiction of the main parameters from the wind direction.

In the second implementation we have chosen a wind direction of 140° in comparison to the North-South straight line, and 740 among the 1431 arcs have been selected

4. the procedure has been repeated considering only the inner cells. Avoiding the boundary effects, the difference in the values of roughness is reduced.

Rocchi Raupach

BottemaMestayer

ResultsResults

Zd – Comparison among the three methods

ResultsResults

Z0 – Comparison among the three methods

Rocchi Raupach

BottemaMestayer

ResultsResults

Rocchi RaupachBottemaMestayerRocchi RaupachBottemaMestayer

Zd– 3D visualization of the comparison among the three methods

Rocchi RaupachBottemaMestayerRocchi RaupachBottemaMestayer

ResultsResults

Z0– 3D visualization of the comparison among the three methods

Rocchi Bottema/Mestayer

Raupach

RocchiRaupach

Rocchi Bottema/Mestayer

Bottema/Mestayer Raupach

Confronto Zd

0

5

10

15

20

25

0 20 40 60 80 100 120 140 160

RugoxelZd

Zd Rocchi

Zd Bottema/Mestayer

Zd Raupach

Confronto Zd

0

5

10

15

20

25

0 20 40 60 80 100 120 140 160

Rugoxel

Zd

Zd Rocchi

Zd Bottema/Mestayer

Zd Raupach

Zd COMPARISON Z0 COMPARISON

ResultsResults

Zd and Z0 as a function of the frontal area density after the exclusion of the “border effects”

Comparison Zo

0

1

2

3

4

5

6

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0


Zo

Comparison Zd

0

5

10

15

20

25

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0


Zd

Comparison Zo

0

1

2

3

4

5

6

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0


Zo

Comparison Zd

0

5

10

15

20

25

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0


Zd

Comparison Zo

0

1

2

3

4

5

6

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0


Zo

Comparison Zd

0

5

10

15

20

25

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0


Zd

Comparison Zd

0

5

10

15

20

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0


Zd

Comparison Zo

0

1

2

3

4

5

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0


Zo

The comparison has been done with a grid cell 2-D 200m x 200m

ResultsResults

Comparison among the obtained results with two different wind directions

Comparison Zo

0

2

4

6

8

10

50 60 70 80 90 100 110

Rugoxel

Z0 Zo(340°)

Zo(140°)

Comparison Zd

0

5

10

15

20

50 60 70 80 90 100 110

Rugoxel

Zd Zd(340°)

Zd(140°)

CONCLUSIONS

By comparing the results, we can observe that the three curves' trend is quite similar while a more sensible difference is detected in the z0 and zd values. Moreover, this difference increases with the lower values of frontal and planar density values. This trend can be explained by analyzing the different approaches adopted in the previous three models.

The Bottema-Mestayer' model is empirical and adopts, as principal parameters, the building's height and their planar density; so it doesn't consider the mutual distance between the building's blocks. Moreover, from many application, it seems that the model tends to return overestimated values with frontal density values greater than 0.2.

The developed procedure, on the contrary, is founded on the analytical evaluation of the mutual distance between buildings and these distances influence, due the weight they have in the model formulation, the results. The analytical adopted approach allows to apply the model in whichever urban context and wind direction.

Few studies are now available, concerning the application of theoretical models of urban roughness parameters estimation at existing urban contexts; so it is quite difficult to fully appreciate the goodness of the obtained results. At this time we are looking for the validation of the procedure by employing it in urban areas already tested with other methods.

Rocchi

Technology

urban canopy layer ucl

ucps building ucps canopy

displacement height

urban installation

urban modelling

calledurban roughness

roughness sublayer rsl

roughness length z d