CAP88-PC V4 Training

1. CAP88-PC V4 Training Module 1.2 Equations Used For Calculating Dose

2. CAP88 Methodology • Calculate values in each sector • Calculate air concentrations in each sector • Calculate deposition rates in each sector • Calculate ground concentrations in each sector • Calculate concentrations in vegetables, milk, and meat produced in each sector • Calculate concentrations in vegetables, milk, and meat ingested by a receptor in each sector • Calculate dose and risk to a receptor in each sector

3. Assessment Area & Sectors CAP88 calculates the dose to receptors in sectors defined user defined rings and the 16 compass directions.

4. Calculation of values • Calculate values in each sector • Calculate air concentrations in each sector • Calculate deposition rates in each sector • Calculate ground concentrations in each sector • Calculate concentrations in vegetables, milk, and meat produced in each sector • Calculate concentrations in vegetables, milk, and meat ingested by a receptor in each sector • Calculate dose and risk to a receptor in each sector

5. Plume Dispersion is the distance downwind is the horizontal dispersion coefficient is the crosswind distance is the vertical dispersion coefficient is the distance above the ground is the effective stack height is the release rate is the distance where is the wind speed

6. Plume Dispersion (continued) Averaging the concentration along the direction: The ground level concentration is found by setting :

7. Dispersion Coefficients

8. Plume Rise is the height of the stack is the plume rise CAP88 provides for four methods for calculating the plume rise: • Buoyant • Momentum • Fixed • None

9. Buoyant Plume Rise For Stability Classes A, B, C, and D:

10. Buoyant Plume Rise For Stability Classes E, F, and G: is the gravitational acceleration is the air temperature is the vertical temperature gradient is the adiabatic lapse rate of atmosphere (0.0098 K/m)

11. Momentum Plume Rise is the effluent stack gas velocity is the inside stack diameter

12. Calculation of Air Concentrations • Calculate values in each sector • Calculate air concentrations in each sector • Calculate deposition rates in each sector • Calculate ground concentrations in each sector • Calculate concentrations in vegetables, milk, and meat produced in each sector • Calculate concentrations in vegetables, milk, and meat ingested by a receptor in each sector • Calculate dose and risk to a receptor in each sector

13. In-Flight Decay/Ingrowth Calculations The atom concentration in air for each radionuclide, , was calculated by solving the following system of ordinary differential equations (ODEs) as a function of time based on the windspeed: is the radioactive decay constant is the physical removal constant is the branching ratio from nuclide to nuclide

14. Calculate of Deposition Rates • Calculate values in each sector • Calculate air concentrations in each sector • Calculate deposition rates in each sector • Calculate ground concentrations in each sector • Calculate concentrations in vegetables, milk, and meat produced in each sector • Calculate concentrations in vegetables, milk, and meat ingested by a receptor in each sector • Calculate dose and risk to receptor in each sector

15. Wet Deposition Rate is average concentration in plume up to lid height is lid height (tropospheric mixing layer) is the scavenging coefficient, calculated by multiplying the rainfall ( in cm y-1) by a constant (10-7 y cm-1 s-1)

16. Dry Deposition Rate is the ground level air concentration is the deposition velocity

17. Plume Depletion For dry deposition: is the gravitational velocity For wet deposition: is the time required to reach the location

18. Calculation of Ground Concentration • Calculate values in each sector • Calculate air concentrations in each sector • Calculate deposition rates in each sector • Calculate ground concentrations in each sector • Calculate concentrations in vegetables, milk, and meat produced in each sector • Calculate concentrations in vegetables, milk, and meat ingested by a receptor in each sector • Calculate dose and risk to a receptor in each sector

19. Ground Surface Decay/Ingrowth Calculations The atom concentration in on the ground surface for each radionuclide, , was calculated by solving the following system of ordinary differential equations (ODEs) as a function of time: is the total deposition rate is the radioactive decay constant is the physical removal constant (2% per year) is the branching ratio from nuclide to nuclide

20. Calculate of Concentrations in Vegetables, Milk, and Meat • Calculate values in each sector • Calculate air concentrations in each sector • Calculate deposition rates in each sector • Calculate ground concentrations in each sector • Calculate concentrations in vegetables, milk, and meat produced in each sector • Calculate concentrations in vegetables, milk, and meat ingested by a receptor in each sector • Calculate dose and risk to receptor in each sector

21. Concentration in Leafy Vegetables • is the deposition rate in sector at distance • the fraction of deposited activity retained on leafy vegetables • is the effective removal constant of the th radionuclide from soil • the concentration uptake factor the th radionuclide for leafy vegetables • is the agricultural productivities by unit area for leafy vegetables • is the radioactive decay constant of the th radionuclide • is the removal constant from plants due to weathering • is the effective surface density of soil (assuming a 15 cm plow layer) • is the period of long-term buildup for activity in sediment or soil • is the time delay between harvest ingestion of leafy vegetables • is fraction of radioactivity retained after washing for leafy vegetables and produce

22. Concentration in Non-Leafy Vegetables • is the deposition rate in sector at distance • the fraction of deposited activity retained on non-leafy vegetables • is the effective removal constant of the th radionuclide from soil • the concentration uptake factor the th radionuclide for non-leafy vegetables • is the agricultural productivities by unit area for non-leafy vegetables • is the radioactive decay constant of the th radionuclide • is the removal constant from plants due to weathering • is the effective surface density of soil (assuming a 15 cm plow layer) • is the period of long-term buildup for activity in sediment or soil • is the time delay between harvest ingestion of non-leafy vegetables

23. Concentration in Pasture Grass • is the deposition rate in sector at distance • the fraction of deposited activity retained on pasture grass • is the effective removal constant of the th radionuclide from soil • the concentration uptake factor the th radionuclide for pasture grass • is the agricultural productivities by unit area for pasture grass • is the radioactive decay constant of the thradionuclide • is the removal constant from plants due to weathering • is the effective surface density of soil (assuming a 15 cm plow layer) • is the period of long-term buildup for activity in sediment or soil • is the time delay between harvest ingestion of pasture grass

24. Concentration in Stored Feed • is the deposition rate in sector at distance • the fraction of deposited activity retained on stored feed • is the effective removal constant of the th radionuclide from soil • the concentration uptake factor the th radionuclide for stored feed • is the agricultural productivities by unit area for stored feed • is the radioactive decay constant of the thradionuclide • is the removal constant from plants due to weathering • is the effective surface density of soil (assuming a 15 cm plow layer) • is the period of long-term buildup for activity in sediment or soil • is the time delay between harvest ingestion of pasture grass

25. Parameter Values

26. Concentration in Animal Feed • is the concentration of the th radionuclide in pasture grass in milk in sector at distance • is the concentration of the th radionuclide in stored feeds in milk in sector at distance • is the fraction of the year that animals graze on pasture • is the fraction of daily feed that is pasture grass when the animal grazes on pasture

27. Concentration in Meat • is the fraction of the animal's daily intake of the th radionuclide which appears in each kilogram of flesh • is the concentration of the th radionuclide in the animal's feed in sector at distance • is the amount of feed consumed by the animal per day • is the radiological decay constant of the thradionuclide • is the average time from slaughter to consumption

28. Concentration in Milk • is the average fraction of the animal's daily intake of the th radionuclide which appears in each liter of milk • is the concentration of the th radionuclide in the animal's feed in sector at distance • is the amount of feed consumed by the animal per day • is the radiological decay constant of the th radionuclide • is the average transport time of the activity from the feed into the milk and to the receptor

29. Calculation of Dose and Risk to a Receptor • Calculate values in each sector • Calculate air concentrations in each sector • Calculate deposition rates in each sector • Calculate ground concentrations in each sector • Calculate concentrations in vegetables, milk, and meat produced in each sector • Calculate concentrations in vegetables, milk, and meat ingested by a receptor in each sector • Calculate dose and risk to a receptor in each sector

30. Average Concentrations in Foods Ingested

31. Agricultural Fractions For population type runs (weighted by area): For individual type runs (unweighted): • the fraction of vegetables grown locally • is the fraction of vegetables grown regionally in the assessment area • the fraction of milk produced locally • is the fraction of milk produced regionally in the assessment area • is the fraction of meat produced locally • is the fraction of meat produced regionally in the assessment area

32. Calculation of Dose and Risk to a Receptor • Calculate values in each sector • Calculate air concentrations in each sector • Calculate deposition rates in each sector • Calculate ground concentrations in each sector • Calculate concentrations in vegetables, milk, and meat produced in each sector • Calculate concentrations in vegetables, milk, and meat ingested by a receptor in each sector • Calculate dose and risk to a receptor in each sector

33. Total Dose Rate • is the external air immersion dose rate the th organ of a receptor in sector at distance • is the external ground surface dose rate the th organ of a receptor in sector at distance • is the internal dose rate the th organ of a receptor in age group in sector at distance from inhalation • is the internal dose rate the th organ of a receptor in age group in sector at distance from ingestion

34. External Dose from Direct Exposure to Activity in the Air (Immersion) • is the air immersion dose factor for the th organ for the thradionuclide • is the air concentration of the thradionuclide

35. External Dose from Ground Surface • is the attenuation factor accounting for shielding provided by residential structures • is the ground surface dose factor for the th organ for the th radionuclide • is the ground concentration of the thradionuclide

36. Internal Dose from Inhalation • is the breathing rate of age group • is the dose conversion factor for the inhalation of the th radionuclide, for the thorganfor age group • is the annual average ground-level concentration of the th radionuclide in air in sector at distance

37. Internal Dose from Ingestion • is the DCF for the ingestion of the th radionuclide, the th organ, & age group • is the concentration of the th radionuclide in non-leafy vegetables • is the concentration of the th radionuclide in milk • is the concentration of the th radionuclide in meat • is the concentration of the th radionuclide in leafy vegetables • is the ingestion rate of non-leafy vegetables, fruit, and grains in age group • is the ingestion rate of milk for individuals in age group • is the ingestion rate of meat for individuals in age group • is the ingestion rate of leafy vegetables for individuals in age group • is the fraction of produce ingested grown in garden of interest • is the fraction of leafy vegetables grown in the garden of interest

38. Ingestion Dose Rate Parameters

39. Population Dose • is the population of age group in sector at distance

40. Total Risk is the external air immersion risk to the th organ of a receptor is the external ground surface risk to the th organ of a receptor is the internal risk to the th organ of a receptor in age group is the internal risk to the th organ of a receptor in age group

41. External Risk from Direct Exposure to Activity in the Air (Immersion) • is the air immersion risk conversion factor for the th organ for the thradionuclide (same for all age groups) • is the air concentration of the thradionuclide

42. External Risk from Ground Surface • is the attenuation factor accounting for shielding provided by residential structures • is the ground surface risk conversion factor for the th organ for the th radionuclide • is the ground concentration of the thradionuclide

43. Internal Risk from Inhalation • is the breathing rate of age group • is the risk conversion factor for the inhalation of the th radionuclide, for the thorganfor age group • is the annual average ground-level concentration of the th radionuclide in air in sector at distance

44. Internal Risk from Ingestion • is the RCF for the ingestion of the th radionuclide, the th organ, & age group • is the concentration of the th radionuclide in non-leafy vegetables • is the concentration of the th radionuclide in milk • is the concentration of the th radionuclide in meat • is the concentration of the th radionuclide in leafy vegetables • is the ingestion rate of non-leafy vegetables, fruit, and grains in age group • is the ingestion rate of milk for individuals in age group • is the ingestion rate of meat for individuals in age group • is the ingestion rate of leafy vegetables for individuals in age group • is the fraction of produce ingested grown in garden of interest • is the fraction of leafy vegetables grown in the garden of interest