Books & Software on Environmental Radioactivity and Pesticides

**Environmental Research & Publications Inc.**

**Mailing Address:**

P.O. BOX: 79023, Garth Postal Outlet,

Hamilton,
Ontario, Canada, L9C 7N6

Business Address:

140 Golden Orchard Drive,

Hamilton, Ontario,
Canada, L9C 6J6

Telephone: (905) 385-8111; Fax: (905) 385-8263; E-mail: porder@enviropu.ca

Environmental Research & Publications
Inc. is pleased to announce the publication of the new SOFTWARE(2015) and
earlier software (2003, 2013) and books as follows:

(1) SOFTWARE(2015):

DIFFUSION COEFFICIENT AND SEDIMENTATION

RATE IN SEA
AND LAKE SEDIMENTS BY ^{(239+240)}Pu AND ^{137}Cs
PROFILES

(Application of the Fourier Solution of Advection Diffusion Equation (ADE)

with Decay Constant, λi, Where Initial Distribution is Given

by Dirac Delta Function, δ(x-0.0))

Dr. B. S. Shukla, Environmental Consultant

***Pb-210 dating of sediments software(2003) with Addendum(2013)***

***is included with the software (2015)***

ISBN 978-0-9696383-8-4 ; Year 2015;

Guide Booklet: 80pp; 8x11; 8 Figures; 33 Tables; 24 Equations.

CDROM: The folder CSPu15 in the CDROM has 11 sub-folders with 241 files

Price in Canada and USA US $169.00/ outside US $189.00. Taxes and postage by air mail are included

This
software(2015) is based on the ADE-PEAK
model as earlier described in the book by Shukla (2010).The software(2015)
computes both the diffusion coefficient of ^{(239+240)}Pu,
D_{Pu}, and sedimentation rate, V_{Pu}, based on
^{(239+240)}Pu profile in the sediment core. The software(2015) also
computes both the diffusion coefficient of ^{137}Cs, D_{Cs}, and
sedimentation rate, V_{Cs}, based on ^{137}Cs profile in the
sediment core. This is the first openly available software based on Fourier
solution of ADE with λi. The results obtained by ADE-PEAK model are compared
with the results of ADE-NUMERICAL model
due to Alperin et al.(2002), Deep -Sea Research
II,49, 4645-4665. Both the models are discussed in the guide booklet.

*FEATURES: The software (2015) is very
efficient because (a) 20 roots of the transcendental equation are internally
generated by bracketing method in a few
seconds (b) the domain length, L(cm),based on Fourier-Shukla Length is generated by software
(c) the error in the material balance is ± 0.2% which is better than ± 0.4% in
ADE-NUMERICAL model. User without any knowledge of Fourier solution and
eigenvalues, can run the software with the help of guide booklet. The software (2015) also
predicts mixing depth.*

Table of Contents of the Guide Booklet

1. Introduction 1

2. Operation of cspudat to prepare data file (1-4)

3.Operation of dela243c to calculate diffusion coefficient,
D_{Cs} and V_{Cs}(4-16)

4. Operation of dela243p and del243c to sea and lake sediment cores (16-28)

5.
Diffusion coefficient, sedimentation rate and sediment dating by
^{(239+240)}Pu,

^{137}Cs
and ^{210}Pb tracers(28-35)

6.Summary and conclusions(35-38)

APPENDIX- A: Solving convergence problem in Fourier solutions of ADE

and development of an efficient software (39-72)

APPENDIX- B: Derivation of ADE solution in finite column for solute

initially distributed as Dirac Delta Function, δ(x-b) (73-76)

REFERENCES (77-79)

SUBJECT INDEX (80)

Technical Requirements: The software(2015) works with Windows XP, 7 and 8 on IBM compatible PC.

Technical
Support: The software(2015) is sold with limited support by Fax,
Telephone and E-mail.

MORE ABOUT THE NEW SOFTWARE PACKAGE (2015):

*The software (2015) has one C.D.ROM
disc marked as ADE-FOURIER(2015) which
has all the programs, data and output filles in the folder CsPu15. The folder CSPu15 has 11 sub-folders
with 241 files. 80 page guide booklet(2015)describes with examples the operation
of the 5 programs, viz., cspudat, dela243c, dela243p,roota26 and dela243. These programs display the results on
the screen and the results can also be saved and printed. *

*In order to authenticate the
software(2015), 23 sediment cores are chosen from the different researchers,
viz., 10 cores from Alperin et al. (2002) Deep-Sea Research II, 49, 4645-4665; 6
cores from Nagaya et al.(1992) J. of Oceanography vol.48, pp 23-35; 4 cores from
Durham et al.(1980) chem. Geol. 31, 53-66; 1 core from Robbins et al.(1975)
Geochim Cosmochim. Acta, 39, 285-304; 1 core from Laissaoui et al.(2008) and 1
core from Nie et al.(2001) Limnol Oceanogr.,46(6)1425-1437. *

*The average values of the D _{Pu} and V_{Pu} for 10
cores by ADE-NUMERICAL model as reported by Alperin et al.(2002) are 1.025
cm^{2}.yr^{-1} and
0.0715 cm.yr^{-1}, respectively, but ADE-PEAK values are 0.76225
cm^{2}.yr^{-1}
and V_{Pu} = 0.1323
cm.yr^{-1}, respectively. Thus, it can be stated that ADE-NUMERICAL model over estimates
the D_{Pu} and under estimates the V_{Pu} in comparison with
ADE-PEAK model. *

*The results of 6 cores modeled from
the works of Nagaya et al.(1992), yielded that D _{Pb} > D_{Pu} > D_{Cs}.
Moreover, it is also found that V_{Pb}> V_{Cs}>
V_{Pu}. Nagaya et al.(1992) reported that D_{Pb} values vary in
wide range from 1.4 to 8.3 cm^{2}.yr^{-1}. From
the ^{210}Pb dating software (2003, 2013) it is confirmed that
D_{Pb} values indeed vary in wide range from 0.0001
cm^{2}.yr^{-1} to 11.00 cm^{2}.yr^{-1} in
these cores. Moreover, based on the
modeling of these cores it is also found that higher V_{Pb} is
associated with higher D_{Pb} in a core. But, D_{Pu} and D_{Cs} in these
cores vary in a narrow ranges from 0.30 cm^{2}.yr^{-1} to
1.79 cm^{2}.yr^{-1}
and 0.29 cm^{2}.yr^{-1} to
1.05 cm^{2}.yr^{-1},
respectively. From the modeling of 23 sediment cores, the Vi and Di values of
^{(239+240)}Pu, ^{137}Cs and ^{210}Pb
are now better organized and explained in the Guide Booklet.*

*ADE-PEAK model is applied to cores due to
Robbins et al.(1975) and Nie et al.(2001) to predict mixing depth. *

*INTENDED SOFTWARE(2015)USERS ARE: scientists, engineers
and researchers in the university/research institute, affiliated with the
department of geology, hydrology, limnology, civil engineering, environment,
marine geology, oceanography, agriculture, nuclear waste, soil physics and
mathematics.*

(2) DIFFUSION COEFFICIENT

AND MIXING DEPTH
THROUGH

ENVIRONMENTAL RADIOACTIVITY

(MODELS AND APPLICATIONS)

** ISBN 978-0-9696383-6-0 ; Year 2010; 331pp; 8x11; 45 Figures; 137 Tables; 365 Equations.
Price in Canada and USA US$ 129.00/ outside US$ 149.00. Taxes and postage by air mail are included.**

**(RELATED TO SOFTWARE ADDENDUM (2013) AND BOOK(2002) ON SEDIMENTATION RATE) **

This book deals with the abinitio derivation of advection diffusion equation (ADE) solutions by Fourier transform and applications of the solutions in the computation of biological diffusion coefficient (Dbi) and mixing depth (Lmi) in lake and sea sediment cores. A new model named as ADE-PEAK model is developed. The results of the ADE-PEAK model are compared with the ADE-STAT model due to Guinasso and Schink (1975) J. Geophys. Res. 80,21,3032-3043 and ADE-APPROXIMATE model due to Officer and Lynch (1983) Marine Geology,52,59-74. The theoretical reason and computation results prove that the ADE-STAT model predicts inaccurate values of Lmi and Dbi. It is also proven that ADE-APPROXIMATE model underestimates Lmi and overestimates Dbi.

**FEATURES:**

It is demonstrated that ADE-PEAK model predicts the most accurate values of Dbi and Lmi. This book also addresses the convergence problem in Fourier solutions as first encountered by Brenner (1962) Chem. Engng. Sci.17, 229-243. This book also addresses an other type of the convergence problem in the application of Fourier solutions, known as Gibbs Phenomenon which occurs at the extremities of the finite length within which the solutions are applicable.

**Table of Contents:**

Chapter 2. EVALUATION OF ADE SOLUTIONS: PART-I (9-70)

Chapter 3. EVALUATION OF ADE SOLUTIONS: PART-II (71-96)

Chapter 4. EVALUATION OF ADE SOLUTIONS: PART-III (97-140)

Chapter 5. APPLICATIONS OF ADE:- PART-I BIOLOGICAL DIFFUSION COEFFICIENTS AND MIXING DEPTH IN SEA SEDIMENT CORES (141-201)

Chapter 6. APPLICATIONS OF ADE:- PART-II BIOLOGICAL DIFFUSION COEFFICIENTS, PEAK VELOCITY AND MIXING DEPTH IN SEDIMENT CORES (202-251)

APPENDIX- A: ADE SOLUTIONS BY FOURIER TRANSFORM (253-322)

REFERENCES (323-327)

AUTHOR INDEX, SUBJECT INDEX and SYMBOLS (328--331)

**MORE ABOUT THE NEW BOOK:**

In Appendix-A, advection diffusion equation (ADE) with decay constant λi is solved by Fourier transform under various initial and boundary conditions. The methodology is based on the standard text books on heat conduction in solids. Scientists, engineers and researchers with the background in physical chemistry, physics and mathematics can very easily understand the steps involved in the derivation of the ADE solutions. Chapters 2, 3 and 4 are devoted to in depth understanding of the profiles of the various ADE solutions by taking fixed values of diffusion coefficient,Di, and advection velocity, Vi, as 0.182 cm^{2}yr^{-1} and 0.182 cm.yr^{-1}, respectively. The exactly same values of Di and Vi were earlier used by Cleary and Adrian (1973) Soil Sci.Soc. Amer. Proc. 37, 197-199. The purpose of using the same Di and Vi values is to authenticate their results as well as the results reported in this book. In chapter 2, λi = 0.0311386 yr^{-1} is used as required for the ^{210}Pb profile, but in chapters 3 and 4, λi = 0.0229747 yr^{-1} is used as required for ^{137}Cs profile. In chapter 2, convergence problem in Fourier solution as related to the Péclet number, (P = Vi L/Di), is solved by defining a suitable length of a column, Lsp, which is named as Fourier-Shukla length. By applying the principle of material balance, and by using the ADE solutions obtained by Laplace transform, it is proven that ADE solutions obtained by Fourier transform can be applied to any P provided Fourier-Shukla length is satisfied. Lsp is a function of Di, Vi, and travel time t. The convergence problem referred to as Gibbs Phenomenon is addressed with the help of Break Through Curve (BTC).The back calculation of Di and Vi by graphical method from the ADE pulse solution profile, proves that the calculated Di and Vi are time dependent and Di and Vi are not equal to 0.182 which is the input value to produce the profile. In chapter 4, back calculation of Di and Vi by statistical moments (s, µ, S), proves that statistical method under predicts Di and over predicts Vi and the values of Di and Vi are not constants but depend on travel time. In chapter 5, results obtained by ADE-STAT, ADE-APPROXIMATE and ADE-PEAK models are compared and relative merits and demerits are explained. ADE-PEAK model is based on the matching of peak position and peak concentration of the field profile with the theoretical profile. ADE-PEAK model quantifies peak velocity and distinguishes between advection velocity, Vi, and peak velocity, Vp. In chapter 6, ADE-PEAK model is applied to determine Dbi and Lmi based on ^{239+240}Pu and ^{137}Cs profiles. In chapter 6, the model due to Goldberg and Koide (1962) Geochim. et Cosmochim. Acta 26,417-450, is also applied to ^{210}Pb profile to determine Dbi and Lmi.

**INTENDED BOOK USERS ARE**: scientists, engineers and researchers in the university/research institute, affiliated with the department of geology, hydrology, limnology, civil engineering, environment, marine geology, oceanography, agriculture, nuclear waste, soil physics and mathematics.

(3) Sedimentation
Rate

Through

Environmental

Radioactivity

(Models and Applications)

Dr. B. S. Shukla,
Environmental Consultant

Click Here To Order

By calculating the uncertainty in the dates of 13 sediment cores, it is found that both the CIC and CRS models predict unreliable dates when variations in the

A. PROPERTIES OF THE STEADY STATE SOLUTIONS.

B. APPROXIMATIONS IN THE ADVECTION-DIFFUSION EQUATION (

C. AUXILIARY EQUATIONS.

D. LINEAR REGRESSION, DATA FILES, COMPUTER PROGRAM AND RESULTS.

ISBN 0-9696383-3-7, 2002, 198pp; 8x11; 7 Figures; 103 Tables; 224 Equations

Price in Canada & USA US$129.00/Outside US$149.00. Taxes and postage by air mail are included.

Both the CIC and CRS models assume constant

**(4) Watershed, River and Lake Modeling through Environmental
Radioactivity.** ISBN 0-9696383-0-2,
1993, 227pp; 8x11; 168 figures; 38 Tables; 197 equations; By B. S. Shukla,
Ph.D.; Price: In Canada & USA US$ 129.00/ Outside US$ 149.00. Taxes and
postage by air mail are included. Payment is accepted in both US$ and equivalent
Canadian dollars.

The above book describes the behaviour of pollutants in watershed, surface waters and bottom sediments of lakes and rivers. In the watershed, the removal of pollutant by runoff, soil erosion and infiltration has been discerned, formulated and exemplified. In the lake and river waters, the removal constants by sedimentation, outflow, food-chain, and biota have been discerned, formulated and exemplified. In the bottom sediments, the removal constants and residence times by diffusion and advection have been discerned, formulated and exemplified. Since this book describes the pollutant behaviour in three distinct but connected boxes, viz., the watershed, the river and lake waters, and the bottom sediments of the river and lake; the models are collectively named as 3-BOX model. The concept of branching decay constants has been invoked to define various removal constants and residence times.

This book applies the mathematics of diffusion - advection coupled with the
first order rate constant and the general mass balance equations to the fallout
and the natural radionuclides present in air, water and soil to predict their
transport and accumulation in watershed soil, sediments, waters and biota. This
is the first book that concurrently quantifies the removal of pollutants both by
runoff and infiltration from watershed soil. The models developed in this book
assume an effective surface soil depth in which pollutants are homogeneously
distributed as introduced in the publication, **Earth and Planetary Science
Letters, 105(1991) 314-318**, co-authored by Dr. B. S. Shukla. The importance
of the book can be seen from the comments that appeared in the **Soil Sci. Soc.
Am. J. 58:991(1994), 58:1848(1994).**

**FEATURES**

(1) The 3-BOX model has been successfully applied to: (a) alpine Rhône
watershed of Switzerland (b) five largest rivers of Finland (c) the Great Miami
River of USA and (d) the chain of the Great Lakes. (2) The radionuclides that
have been employed in the modeling are: ^{7}Be, ^{210}Pb,
^{90}Sr, ^{137}Cs, and ^{239+240}Pu.

CONTENTS

(i) Objectives and scope of the book

(ii) Basic concepts in aquatic modeling

(iii) Mathematics of 3-BOX model of river system

(iv) Application of ^{7}Be and ^{210}Pb in soil
erosion

(v) ^{90}Sr, ^{137}Cs and ^{239+240}Pu
transport from watershed to river waters

(vi) Application of the 3-BOX model to the Great Lakes.

**RELEVANCE OF THE ABOVE BOOK TO NUCLEAR WASTE DISPOSAL**

Nuclear research centres throughout the world have been conducting many experimental and theoretical studies on the various aspects of the safe disposal of the high level nuclear waste since the inception of the peaceful uses of the nuclear energy. Nuclear waste forms can be either the spent fuel itself or a glass-ceramics containing the fission products and the a emitters. The waste form will finally have to be put to the rest in a deep geological formation.

The waste form in the geological formation may come in contact with the
infiltrating water and release ^{239+240}Pu, ^{137}Cs and
^{90}Sr by leaching processes. The leachate containing
^{239+240}Pu, ^{137}Cs and ^{90}Sr will eventually
migrate through aquifer and pollute the charging surface waters. The radioactive
contaminants in the surface waters will end up in the food chain through
drinking water and fish harvesting. The possibility of food chain contamination
by these radionuclides has prompted the development of food chain models and the
extensive study on the leaching of these radionuclides from the waste forms.

This book deals with the leaching and migration of ^{239+240}Pu,
^{137}Cs and ^{90}Sr that have been deposited on the soil as a
result of atmospheric nuclear weapon testing which peaked during 1963-1964.
Significant quantities of weapon produced radionuclides have been falling on the
soil and surface waters since 1954 till now. The rain water removes the
atmospherically deposited ^{239+240}Pu, ^{137}Cs and
^{90}Sr to surface waters by runoff and to ground waters by
infiltration. This book describes the mathematical models and the results of the
calculation pertaining to the removal of the atmospherically deposited
^{239+240}Pu, ^{137}Cs and ^{90}Sr from seven watershed
soils by rainwater via infiltration and runoff. The book also describes the
partitioning of these radionuclides among biota, waters, sediments which in turn
will be useful in evaluating the radiation doses to the general public through
fish and water consumption. This is the first book that employs the naturally
produced ^{210}Pb and ^{7}Be to estimate the soil erosion and
other environmental parameters. The book is expected to be useful for the
engineers, scientists, managers, and educators working in the field of nuclear
waste management, health physics and soil physics, for years to come.

**INTENDED BOOK USERS ARE:** scientists, engineers and
researchers in the university/ research institute affiliated with the
departments of nuclear waste, hydrology, civil engineering, environment,
agriculture, pesticides, the Great Lakes and limnology.

**(5) Transport of Pesticides from Watershed by Volatilization, Infiltration
and Runoff** ( Models and applications).
ISBN 0-9696383-2-9, 1996, 187pp; 8x11; 64 figures; 36 Tables; 306 equations; By
B. S. Shukla, Ph.D.; Price: In Canada & USA US$ 129.00/ Outside US$ 149.00.
Taxes and postage by air mail are included. Payment is accepted in both US$ and
equivalent Canadian dollars.

The above book describes the use of the analytical solutions of the Advection
diffusion equation (ADE) involving first order degradation constant
(l ), in
predicting the transport of pesticides from land to air, sub-surface waters, and
surface waters by volatilization, infiltration and runoff, respectively. All the
steps involved in the derivation of ADE for unsaturated soil are clearly stated.
The method of Laplace transforms in solving the ADE is exemplified under
different initial and boundary conditions. The analytical solutions of ADE are
applied to explain the break through curves and slug movement of the degrading
pollutants. New models have been developed and successfully applied to explain
the volatilization of pesticides with low and high values of Henry's Law
constant, K_{H}. Equations to estimate l in presence of volatilization are also given. The name
5-Box model implies that pesticides applied on the soil can redistribute
themselves among 5 boxes. Box-1, Box-2, Box-3, Box-4 and Box-5 correspond to
watershed, surface waters, sediments, sub-surface waters and atmosphere,
respectively. The equations and examples given in the book will be useful in
initiating and planning new experiments on pollutant transport in the laboratory
as well as in the field.

This is a multidisciplinary book. The book applies the
mathematics of diffusion -advection coupled with the first order rate constant
and the general mass balance equations to predict the transport of pesticides
from watershed by volatilization, infiltration and runoff. The models developed
in this book can be easily extended to the radioactive pollutants. This is the
first book that concurrently quantifies the removal of pollutants by
volatilization, infiltration and runoff from the watershed soil. The models
developed in this book assume an effective surface soil depth in which
pollutants are homogeneously distributed as introduced in the publication,
**Earth and Planetary Science Letters, 105(1991) 314-318**, co-authored by
Dr. B. S. Shukla and in the book "**Watershed, River and Lake Modeling through
Environmental Radioactivity, ISBN 0-9696383-0-2, 1993**" by Dr. B.S.Shukla.
Both the books are complementary to each other and give complete insight into
the mathematical modeling of the transport processes that govern the movement of
pollutants in natural and laboratory setups.

An addendum is also included with the book. The addendum to the book
describes (i) the application of 5-Box screening model to 238 pesticides (ii)
new and original equations that correlate % removal of a pesticide by runoff at
the edge of field (R_{E}), % removal of the pesticide by runoff at the
mouth of the river (R_{M}) in the basin and the ratio (g) of total farmland in the basin to total pesticide
application area in the basin and (iii) the importance of the measurement of the
frequency of appearance (F.A.) of pesticides in rivers. The new models developed
in the addendum have been tested on the field data available in literature
pertaining to the Grand, Saugeen and Thames rivers of Ontario, Canada. The
predictions made by the models are in excellent agreement with the measured
values.

**FEATURES**

Breakthrough curves, concentration profiles in soil columns, volatilization
of low and high K_{H} pesticides, runoff and slug movements. 61
Pesticides have been arranged in the ascending order of their
K_{oc}/t_{1/2} ratio and have been evaluated by various
screening models.

**CONTENTS**:

(i) Objectives and Scope of the Book

(ii) Mathematics of 5-BOX Model

(iii) Research Models with Applications

(iv) Screening Models with Applications

(v) Future Research and Modeling Needs

(vi) Appendix-A: Derivation of advection diffusion equation (ADE) for unsaturated soil.

(vii) Appendix-B: Solutions of the ADE by Laplace Transforms.

(viii) Appendix-C: A few solutions of the ADE.

MORE ABOUT THE ABOVE BOOK

Pesticides have been playing the vital role in the augmentation of agri-food production. There is need to produce more agri-food to cope up with the growing world population. Pesticides will remain an essential part of the modern agriculture and, therefore, their transport from agricultural fields to surface waters, groundwater and air has to be monitored and fully understood. The research into the transport of pesticide by volatilization, infiltration and runoff is in evolutionary state. Both the theoretical and experimental works are not yet well organized as in the other fields of science. This book aims at providing the sound theoretical background for the subject which in turn is required to conduct future laboratory and field studies on the pesticide transport in the environment. The important results described in the book are as follows.

(1) The analytical solutions of ADE to predict BTC, slug movements and
concentration profiles of pesticides in an unsaturated soil are fully explained.
(2) The profiles of slug having different D_{i}, V_{i} and
l
_{i} are compared with the normal distribution curve and interesting
results are obtained. (3) Volatilization of low Henry's constant, K_{H},
pesticides is objectively explained based on the thin pesticide rich soil
surface layer rather than on the presence of a stagnant thin air layer on the
soil surface as assumed previously by other authors. In absence of advection,
the cumulative volatilization of soil incorporated pesticide is shown to be
proportional to Ö D_{i}/Ö l _{i} ratio, and,
therefore, the volatilization behaviour should be assessed by D_{i},
V_{i} and l _{i} and not by K_{H} which
generally contributes very little to D_{i} and V_{i}. (4)
Equation is derived to make correction for volatilization loss while determining
the degradation constant in laboratory. The two slopes observed in the pesticide
decay curve in laboratory study are explained and formulated. It is shown that
in the field scenario, pesticide is lost by infiltration, volatilization, runoff
and degradation and, therefore, the t_{1/2} values determined from the
field study are low and unreliable. (5) Many new equations are derived under
research and screening models. (6) Pesticides are arranged according to the
ascending order of their K_{oc} (mlg^{-1})/t_{1/2}(days)
ratio and it is shown that pesticides with K_{oc}/t_{1/2}
³ 20 are not
threat to air, water and soil pollution. However, pesticides with
K_{oc}/t_{1/2} £ 20 should be judged on the basis of organic matter
content in the soil and rain fall in the region.(7) Appendices A, B, C, and D
give all about ADE, its analytical solutions and the computer program to compute
erf(x), erfc(x) and e^{A}erfc(x).

**INTENDED BOOK USERS ARE**: scientists, engineers, and
researchers in the university/research institute, affiliated with the
departments of pesticides, hydrology, civil engineering, environment,
agriculture, nuclear waste, soil physics and mathematics.

**(6)SOFTWARE(2003),ADDENDUM (2013):****Pb-210 Dating of Sediments **:(Sedimentation Rate through Environmental
Radioactivity: Part-I): ISBN 0-9696383-5-3, **2003-2013**; By B. S. Shukla,
Ph.D.; In Canada & USA US$ 129.00/ Outside US$ 149.00. Taxes and postage by
air mail are included. Payment is accepted in both US$ and equivalent Canadian
dollars.

The software developed in 2003 is expanded by including a 15 page **ADDENDUM (2013)**. Now the C.D.Rom (2003) has two folders **Pbdates** and **Pbdates3** on it. The C.D.Rom(2003) has also the ADDENDUM (2013) file in PDF format on it. Both the folders **Pbdates** and **Pbdates3** have application programs **coredat2** and **corecal2** to compute the Pb-210 dates and related parameters by five models, viz., Constant Initial Concentration(CIC), Constant Rate of Supply (CRS), Advection Diffusion Equation(ADE), Porosity Variation (PV), and Porosity Variation Without Diffusion (PVWD) models. However, **Pbdates3** folder has two additional application programs **vmaxd3** and **vid3**, based on ADE model, to calculate ^{ 210}Pb diffusion coefficient in the sediment core. The user **guide booklet (2003)** describes all the programs, their operation, mathematical background and interpretation of the results. However, ADDENDUM(2013) describes only four application programs: **coredat2**, **corecal2**, **vmaxd3** and **vid3** which are more than sufficient for computing all the results given in** guide booklet**(2003).Operation of these four programs given in **Pbdates3** folder, is fully described in **ADDENDUM (2013)** but briefly summarized as follows.

(1) **coredat2**: This program is used to create data file for ^{ 210}Pb profile in the sediment core. Data file can be corrected by **WordPerfect-12** or **Notepad** and then saved as a file with **.txt** extension which is compatible with the program corecal2. The number of slices in the core must be 35 or less, because corecal2 is programmed to process a data file which has 35 or less ^{ 210}Pb data points.

(2) **corecal2**: The operation of this program is very well documented in users **guide booklet** (2003) and in **ADDENDUM (2013)**.

(3) **vmaxd3** and **vid3**: These programs calculate diffusion coefficient of ^{ 210}Pb based on ADE model. The operation of these programs is completely described in ADDENDUM (2013). The sedimentation rate by ^{137}Cs profile is correct or incorrect can be easily proven with the help of program vid3. For six cores in which ^{137}Cs and ^{ 210}Pb profiles are known, it is found that the ^{137}Cs diffusion coefficient, DCs (cm2.yr-1), varies from 0.75 to 0.02 whereas the ^{ 210}Pb diffusion coefficient, D_{Pb} (cm2.yr-1) varies from 0.14 to 0.0002. Thus, DCs/D_{Pb} ranges from 5.36 to 100. The preceding DCs/D_{Pb} ratio has **theoretical justification** as given in the ADDENDUM (2013) .

FEATURES

^{210}Pb dates, relative uncertainty in dates and variable sedimentation rates and all other parameters based on the 5 models (b) diffusion coefficient by ADE and PV models (2) Results are immediately displayed on the screen and stored in a file to get hard copy (3) Examples to prepare data file, to run the programs and to interpret the results. (4)The application program vid3 described in the addendum(2013) is used to calculate almost exact value of diffusion coefficient of ^{210}Pb in sediment cores and results are compared with other models that compute diffusion coefficient of ^{210}Pb. (5) Suitable for both research and routine uses.

TECHNICAL REQUIREMENTS

**Pbdates3** folder from CD-ROM drive to C: drive or USB: drive. The application programs **coredat2**, **corecal2**, **vmaxd3** and **vid3** are run from CD-ROM drive or C: drive or USB drive by Windows **XP**, **7** **and 8** on IBM compatible PC. The data files and result files are to be written on the C: drive or USB: drive. The steps involved in running of the programs are fully explained in the **Addendum (2013)**.

**TECHNICAL SUPPORT **