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Discussion space - W3: Simulation of environmentally relevant behaviour with Agent Based Modelling: From real systems to conceptual models

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'''Position paper under discussion''': [[W3-PositionPaper-v1.pdf| PositionPaperBinderetal080122.pdf]]
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'''Position paper under discussion''': [[Attach:PositionPaperBinderetal080122.pdf| PositionPaperBinderetal080122.pdf]]
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'''Position paper under discussion''': [[W3-PositionPaper-v1.pdf| W3-PositionPaper-v1.pdf]]
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'''Position paper under discussion''': [[W3-PositionPaper-v1.pdf| PositionPaperBinderetal080122.pdf]]
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'''Position paper under discussion''': [[Attach:positionPaper.pdf| W3-PositionPaper-v1.pdf]]
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'''Position paper under discussion''': [[W3-PositionPaper-v1.pdf| W3-PositionPaper-v1.pdf]]
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'''Position paper under discussion''': [[Attach:positionPaper.pdf| WorkshopPaper.pdf]]
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'''Position paper under discussion''': [[Attach:positionPaper.pdf| W3-PositionPaper-v1.pdf]]
January 21, 2008, at 06:58 AM by ProfDr P Kumar -
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17:20 by '''[[~Dr P Kumar]]'''
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06:58 by '''[[~Prof(Dr) P Kumar]]'''
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Let the total quantity of the pollutant released from the source within finite time interval = Q (unknown) (1)

For the purpose of testing our model we assume total weight of dust initially released from source = 100 units.

Based on this assumption let the predicted pollutant amount, by the model, at point DS-2 vide Figure (1) be P2
.

But predicted dust amount will be different than actual amount of pollutant collected at point- 2 since actual pollutant was Q and not 100 units. Also let the quantity of actual measured pollutant at
this point be A2.
When P2 is
the predicted pollutant quantity at point DS-2 then the original total pollutant quantity at source is = 100 units.
Hence when A2 is the actually
collected quantity of pollutant at point DS-2 then the total pollutant at original source = (100/P2) x A2 = (Say) (2)
to:
Let the total quantity of the pollutant released from the source within finite time interval = Q (unknown) (1)

For the purpose of testing our model we assume total weight of dust initially released from source
= 100 units.

Based on
this assumption let the predicted pollutant amount, by the model, at point DS-2 vide Figure (1) be P2. But predicted dust amount will be different than actual amount of pollutant collected at point- 2 since actual pollutant was Q and not 100 units. Also let the quantity of actual measured pollutant at this point be A2. When P2 is the predicted pollutant quantity at point DS-2 then the original total pollutant quantity at source is = 100 units.
Hence when A2 is the actually collected quantity of pollutant at point DS-2 then the total pollutant at original source
= (100/P2) x A2 = (Say) (2)
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Hence Q  = (100/ P2) x A2 (3)
to:
Hence Q  = (100/ P2) x A2 (3)
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Table - 2
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(A2 A4)/A3 5.20 x 10-3
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(A2 A4)/A3 5.20 x 10-3
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(P2 P4)/P3 1.33 x 10 -3


(A2 A4)/A3 5.20 x 10-3
SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 2.39 (P2 P4)/P3 2.17 x 10 -3



(A2 A4)/A3
5.20 x 10-3
to:
(P2 P4)/P3 1.33 x 10 -3


(A2 A4)/A3 5.20 x 10-3
SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 2.39 (P2 P4)/P3 2.17 x 10 -3

(A2 A4)/A3
5.20 x 10-3
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(P2 P4)/P3 3.93 x 10 -3
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3. CONCLUSIONS
to:
3. CONCLUSIONS
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16:41 by '''[[~Dr P Kumar]]'''
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(A2 A4)/A3 5.20 x 10-3
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(P2 P4)/P3 1.33 x 10 -3


(A2 A4)/A3 5.20 x 10-3
SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 2.39 (P2 P4)/P3 2.17 x 10 -3

(A2 A4)/A3
5.20 x 10-3
to:
(P2 P4)/P3 1.33 x 10 -3


(A2 A4)/A3 5.20 x 10-3
SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 2.39 (P2 P4)/P3 2.17 x 10 -3



(A2 A4)/A3
5.20 x 10-3
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(P2 P4)/P3 3.93 x 10 -3
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(P2 P4)/P3 3.93 x 10 -3
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!!!!19 January 2008
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16:41 by '''[[~Dr P Kumar]]'''
Experimental Technique of Calibration of Symmetrical Air Pollution Models

P Kumar
MIT College of Engineering,Pune,India
( pkumarmbm@yahoo.com)

1. PRINCIPLE OF COMPUTING SAPMI

It is generally assumed that unless horizontal wind shear persists, at or near the source of release of pollutants, the property of horizontal symmetry on either side of the central line (drawn downwind from the source) is maintained - may it be plume or puff model for point, line or area sources. This concept could be used while developing the index SAPMI. This index is based on the experiment described in this paper, on the concept of dispersion-symmetry, by placing the receivers away from the source point, at and on either side of the central line of the plume, at equal lateral-distances from the line, as shown in figure 1.









Figure-1. BP is the blast point. BP to DS-2 is the direction of the wind marked by arrow. Line DS1 to DS3 is at right angle to line joining BP and DS2 . Point DS2 bisects the line joining DS1 and DS3 . Distances between BP to DS2 , DS2 to DS1 and DS2 to DS3 are 200 m, 50m and 50m respectively.



For the purpose of testing our model we assume total weight of dust initially released from source = 100 units.

Based on this assumption let the predicted pollutant amount, by the model, at point DS-2 vide Figure (1) be P2.

But predicted dust amount will be different than actual amount of pollutant collected at point- 2 since actual pollutant was Q and not 100 units. Also let the quantity of actual measured pollutant at this point be A2.
When P2 is the predicted pollutant quantity at point DS-2 then the original total pollutant quantity at source is = 100 units.

But original quantity of pollutant (Q) will not be same as obtained in equation (2) due to probable prediction-error eM (say) in the model - if the model is incorrect.



Hence after adding the correction eM with the predicted value P2 we get

Total quantity Q computed by (4) can be used to predict the quantity of pollutant at site DS-1 and site DS-3
as(P1xA2)/(P2+eM) and  (P3 x A2) / (P2 + eM) respectively. Symmetry in dispersion process as per the model however provides that error in the measurement and the prediction at site 1 & 3 should also be equal.



Solving equation (5) for eM we get



Equation (6) gives the quantity of error in the model. Hence for the condition of no error, i.e. for eM = 0, equating (6) to zero we obtain the condition for accuracy of the model

i.e. (A1-A3)/A2 = (P1-P3)/P2

(A1-A3)/A2

(P1-P3)/P2
Equation (7) gives the condition of the accuracy of the prediction made by any model. Thus if,

SAPMI = 1 (prediction is accurate)
< 1 (Model is overestimating)
>1 (Model is underestimating)
2. Discussion:



Table - 2
Type of Model Computed SAPMI values

Model-I


Model-II

Model-III

SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 3.9







SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 1.32


SAPMI values decreased from 3.9 to 2.39 in Model-II as the undulated topography was incorporated in Model-I. More perfection in the model, however, was achieved in Model-III with the introduction of topography, ground response and vertical wind shear. This brought down the SAPMI value from 2.39 to 1.32. Still, we observe, that its value is not exactly unity. This may be due to inherent limitations in the assumptions that vertical dust cloud has uniform distribution of dust-density and many experimental or observational errors which affect the numerator of the SAPMI computation values. They could be as under.


(a) Incorrect identification of central line of plume.

(b) Different rate of suction by different dust-samplers due to variation in the manometer readings in the field.

(c) Assumption of constant wind with height.

(d) Difference in elevation of dust samplers kept at sites 2, 3 & 4 due to variation in ground contour in the field.

(e) Fugitive loose dust (sucked in the instrument) may affect the accuracy.. Further such a fugitive dust error may not be uniform for all the sites

Beside experimental causes there could be mathematical approximation errors, too, as follows :-

a) Neglect of thickness of the vertical dust column.

b) Application of reflection property with the assumption that the height of the blast column is of higher order than the order of variation in the ground contour elevation.


3. CONCLUSIONS

(a) Symmetrical Air Pollution Model Index
SAPMI = {((A2-A4)/A3)/((P2-P4)/P3)}
is useful parameter to test the accuracy of predictions made by the models where initial mass of vertical column is unknown.
(b) With gradual improvement in physics of the model SAPMI value gradually approaches to unity.
(c) Once the extent of model accuracy is established, its inaccuracy range could be accordingly accounted while interpreting the results of the predictions.
(d) Even if at the application stage of the model, initial quantity of pollutants released at the source point is accurately known the predictions with the model would not be correct unless SAPMI value is equal to one.


>><<

>>message<<
Changed lines 17-18 from:
!!!!19 January 2008
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!!!!20 January 2008
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16:41 by '''[[~Dr P Kumar]]'''
to:
17:20 by '''[[~Dr P Kumar]]'''
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(A2 A4)/A3 5.20 x 10-3
to:
(A2 A4)/A3 5.20 x 10-3
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(P2 P4)/P3 1.33 x 10 -3


(A2 A4)/A3 5.20 x 10-3
SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 2.39 (P2 P4)/P3 2.17 x 10 -3

(A2 A4)/A3
5.20 x 10-3
to:
(P2 P4)/P3 1.33 x 10 -3


(A2 A4)/A3 5.20 x 10-3
SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 2.39 (P2 P4)/P3 2.17 x 10 -3



(A2 A4)/A3
5.20 x 10-3
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(P2 P4)/P3 3.93 x 10 -3
to:
(P2 P4)/P3 3.93 x 10 -3
Added lines 138-139:
!!!!19 January 2008
Added lines 141-255:
16:41 by '''[[~Dr P Kumar]]'''
Experimental Technique of Calibration of Symmetrical Air Pollution Models

P Kumar
MIT College of Engineering,Pune,India
( pkumarmbm@yahoo.com)

1. PRINCIPLE OF COMPUTING SAPMI

It is generally assumed that unless horizontal wind shear persists, at or near the source of release of pollutants, the property of horizontal symmetry on either side of the central line (drawn downwind from the source) is maintained - may it be plume or puff model for point, line or area sources. This concept could be used while developing the index SAPMI. This index is based on the experiment described in this paper, on the concept of dispersion-symmetry, by placing the receivers away from the source point, at and on either side of the central line of the plume, at equal lateral-distances from the line, as shown in figure 1.









Figure-1. BP is the blast point. BP to DS-2 is the direction of the wind marked by arrow. Line DS1 to DS3 is at right angle to line joining BP and DS2 . Point DS2 bisects the line joining DS1 and DS3 . Distances between BP to DS2 , DS2 to DS1 and DS2 to DS3 are 200 m, 50m and 50m respectively.



For the purpose of testing our model we assume total weight of dust initially released from source = 100 units.

Based on this assumption let the predicted pollutant amount, by the model, at point DS-2 vide Figure (1) be P2.

But predicted dust amount will be different than actual amount of pollutant collected at point- 2 since actual pollutant was Q and not 100 units. Also let the quantity of actual measured pollutant at this point be A2.
When P2 is the predicted pollutant quantity at point DS-2 then the original total pollutant quantity at source is = 100 units.

But original quantity of pollutant (Q) will not be same as obtained in equation (2) due to probable prediction-error eM (say) in the model - if the model is incorrect.



Hence after adding the correction eM with the predicted value P2 we get

Total quantity Q computed by (4) can be used to predict the quantity of pollutant at site DS-1 and site DS-3
as&#61563;(P1xA2)/(P2+eM)&#61565; and &#61563; (P3 x A2) / (P2 + eM) &#61565;respectively. Symmetry in dispersion process as per the model however provides that error in the measurement and the prediction at site 1 & 3 should also be equal.



Solving equation (5) for eM we get



Equation (6) gives the quantity of error in the model. Hence for the condition of no error, i.e. for eM = 0, equating (6) to zero we obtain the condition for accuracy of the model

i.e. (A1-A3)/A2 = (P1-P3)/P2

(A1-A3)/A2

(P1-P3)/P2
Equation (7) gives the condition of the accuracy of the prediction made by any model. Thus if,

SAPMI = 1 (prediction is accurate)
< 1 (Model is overestimating)
>1 (Model is underestimating)
2. Discussion:



Table - 2
Type of Model Computed SAPMI values

Model-I


Model-II

Model-III

SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 3.9







SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 1.32


SAPMI values decreased from 3.9 to 2.39 in Model-II as the undulated topography was incorporated in Model-I. More perfection in the model, however, was achieved in Model-III with the introduction of topography, ground response and vertical wind shear. This brought down the SAPMI value from 2.39 to 1.32. Still, we observe, that its value is not exactly unity. This may be due to inherent limitations in the assumptions that vertical dust cloud has uniform distribution of dust-density and many experimental or observational errors which affect the numerator of the SAPMI computation values. They could be as under.


(a) Incorrect identification of central line of plume.

(b) Different rate of suction by different dust-samplers due to variation in the manometer readings in the field.

(c) Assumption of constant wind with height.

(d) Difference in elevation of dust samplers kept at sites 2, 3 & 4 due to variation in ground contour in the field.

(e) Fugitive loose dust (sucked in the instrument) may affect the accuracy.. Further such a fugitive dust error may not be uniform for all the sites

Beside experimental causes there could be mathematical approximation errors, too, as follows :-

a) Neglect of thickness of the vertical dust column.

b) Application of reflection property with the assumption that the height of the blast column is of higher order than the order of variation in the ground contour elevation.


3. CONCLUSIONS

(a) Symmetrical Air Pollution Model Index
SAPMI = {((A2-A4)/A3)/((P2-P4)/P3)}
is useful parameter to test the accuracy of predictions made by the models where initial mass of vertical column is unknown.
(b) With gradual improvement in physics of the model SAPMI value gradually approaches to unity.
(c) Once the extent of model accuracy is established, its inaccuracy range could be accordingly accounted while interpreting the results of the predictions.
(d) Even if at the application stage of the model, initial quantity of pollutants released at the source point is accurately known the predictions with the model would not be correct unless SAPMI value is equal to one.


>><<

>>message<<
Added lines 20-134:
16:41 by '''[[~Dr P Kumar]]'''
Experimental Technique of Calibration of Symmetrical Air Pollution Models

P Kumar
MIT College of Engineering,Pune,India
( pkumarmbm@yahoo.com)

1. PRINCIPLE OF COMPUTING SAPMI

It is generally assumed that unless horizontal wind shear persists, at or near the source of release of pollutants, the property of horizontal symmetry on either side of the central line (drawn downwind from the source) is maintained - may it be plume or puff model for point, line or area sources. This concept could be used while developing the index SAPMI. This index is based on the experiment described in this paper, on the concept of dispersion-symmetry, by placing the receivers away from the source point, at and on either side of the central line of the plume, at equal lateral-distances from the line, as shown in figure 1.









Figure-1. BP is the blast point. BP to DS-2 is the direction of the wind marked by arrow. Line DS1 to DS3 is at right angle to line joining BP and DS2 . Point DS2 bisects the line joining DS1 and DS3 . Distances between BP to DS2 , DS2 to DS1 and DS2 to DS3 are 200 m, 50m and 50m respectively.



For the purpose of testing our model we assume total weight of dust initially released from source = 100 units.

Based on this assumption let the predicted pollutant amount, by the model, at point DS-2 vide Figure (1) be P2.

But predicted dust amount will be different than actual amount of pollutant collected at point- 2 since actual pollutant was Q and not 100 units. Also let the quantity of actual measured pollutant at this point be A2.
When P2 is the predicted pollutant quantity at point DS-2 then the original total pollutant quantity at source is = 100 units.

But original quantity of pollutant (Q) will not be same as obtained in equation (2) due to probable prediction-error eM (say) in the model - if the model is incorrect.



Hence after adding the correction eM with the predicted value P2 we get

Total quantity Q computed by (4) can be used to predict the quantity of pollutant at site DS-1 and site DS-3
as&#61563;(P1xA2)/(P2+eM)&#61565; and &#61563; (P3 x A2) / (P2 + eM) &#61565;respectively. Symmetry in dispersion process as per the model however provides that error in the measurement and the prediction at site 1 & 3 should also be equal.



Solving equation (5) for eM we get



Equation (6) gives the quantity of error in the model. Hence for the condition of no error, i.e. for eM = 0, equating (6) to zero we obtain the condition for accuracy of the model

i.e. (A1-A3)/A2 = (P1-P3)/P2

(A1-A3)/A2

(P1-P3)/P2
Equation (7) gives the condition of the accuracy of the prediction made by any model. Thus if,

SAPMI = 1 (prediction is accurate)
< 1 (Model is overestimating)
>1 (Model is underestimating)
2. Discussion:



Table - 2
Type of Model Computed SAPMI values

Model-I


Model-II

Model-III

SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 3.9







SAPMI = - - - - - - - - - - = - - - - - - - - - - - = 1.32


SAPMI values decreased from 3.9 to 2.39 in Model-II as the undulated topography was incorporated in Model-I. More perfection in the model, however, was achieved in Model-III with the introduction of topography, ground response and vertical wind shear. This brought down the SAPMI value from 2.39 to 1.32. Still, we observe, that its value is not exactly unity. This may be due to inherent limitations in the assumptions that vertical dust cloud has uniform distribution of dust-density and many experimental or observational errors which affect the numerator of the SAPMI computation values. They could be as under.


(a) Incorrect identification of central line of plume.

(b) Different rate of suction by different dust-samplers due to variation in the manometer readings in the field.

(c) Assumption of constant wind with height.

(d) Difference in elevation of dust samplers kept at sites 2, 3 & 4 due to variation in ground contour in the field.

(e) Fugitive loose dust (sucked in the instrument) may affect the accuracy.. Further such a fugitive dust error may not be uniform for all the sites

Beside experimental causes there could be mathematical approximation errors, too, as follows :-

a) Neglect of thickness of the vertical dust column.

b) Application of reflection property with the assumption that the height of the blast column is of higher order than the order of variation in the ground contour elevation.


3. CONCLUSIONS

(a) Symmetrical Air Pollution Model Index
SAPMI = {((A2-A4)/A3)/((P2-P4)/P3)}
is useful parameter to test the accuracy of predictions made by the models where initial mass of vertical column is unknown.
(b) With gradual improvement in physics of the model SAPMI value gradually approaches to unity.
(c) Once the extent of model accuracy is established, its inaccuracy range could be accordingly accounted while interpreting the results of the predictions.
(d) Even if at the application stage of the model, initial quantity of pollutants released at the source point is accurately known the predictions with the model would not be correct unless SAPMI value is equal to one.


>><<

>>message<<
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(:commentbox:)
to:
(:commentbox:)
!!!!19 January 2008

>>message<<
16:38 by '''[[~Dr P Kumar]]'''
I want to contibute following paper:-

"Experimental Technique of Calibration of Symmetrical Air Pollution Models"
Your permission needed, please.
pkumarmbm@yahoo.com
>><<
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[++'''Position Paper'''++]
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'''Position paper under discussion''': [[Attach:positionPaper.pdf| Workshop1Paper.pdf]]
to:
'''Position paper under discussion''': [[Attach:positionPaper.pdf| WorkshopPaper.pdf]]
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(:title Discussion space - W3: Simulation of environmentally relevant behaviour with Agent Based Modelling: From real systems to conceptual models :)

'''Position paper under discussion''': [[Attach:positionPaper.pdf| Workshop1Paper.pdf]]

[++'''Abstracts'''++]

'''Example of abstract''': [[Attach:abstracExample.pdf| AbstractExample.pdf]]

[++'''Discussion'''++]

Comments from participants.


(:commentbox:)