TECHNICAL PAPERS
Nov 1, 1988

Weather Input for Nonpoint‐Source Pollution Models

Publication: Journal of Irrigation and Drainage Engineering
Volume 114, Issue 4

Abstract

Three stochastic weather models are developed for use with nonpoint‐source pollution simulation models that require sequences of daily precipitation and mean daily temperature. Two simple models have parameters that can be estimated from available secondary data. Both generate temperature and precipitation independently. A third model represents a more sophisticated approach and requires primary data for parameter estimation. A model validation analysis was attempted using three U.S. weather stations. The first two models did not reproduce the higher‐order moments or the tail of the wet‐dry precipitation distribution. All models used normal temperature distributions which did not reproduce the higher‐order moments of the observed temperature distributions. Using historical and generated weather data as input to the Cornell Nutrient Simulation model, annual runoff and percolation, and dissolved nitrogen and phosphorus losses were compared. The third model gave output that was not statistically different from that obtained with the historical weather data; the first two models occasionally gave statistically different values. Using the mean annual losses given by historical weather data as a basis, model errors were less than 20%.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Akaike, H. (1972). “Information theory and an extension of the maximum likelihood principle.” International symposium on information theory, B. N. Petrov and F. Csaki, eds., Akadémiai, Kiadó, Budapest, Hungary, 267–281.
2.
Box, G. E. P., and Jenkins, G. M. (1976). Time series analysis: forecasting and control. Holden‐Day, San Francisco, Calif.
3.
Bridges, T. C., and Haan, C. T. (1972). “Reliability of precipitation probabilities estimated from the gamma distribution.” Monthly Weather Rev., 100(8), 607–611.
4.
Bruhn, J. A., Fry, W. E., and Fick, G. W. (1979). “Weather: a stochastic simulation model of daily weather. Users manual.” Mimeo 79‐1, Dept. of Plant Pathology, Cornell Univ., Ithaca, N.Y.
5.
Buishand, T. A. (1978). “Some remarks on the use of daily rainfall models.” J. Hydrol., 36(3/4), 295–308.
6.
Carey, D. I., and Haan, C. T. (1978). “Markov process for simulating daily point rainfall.” J. Irrig. Drain. Div., ASCE, 104(1), 111–125.
7.
Caskey, J. E. (1963). “A Markov chain model for the probability of precipitation occurrence in intervals of various length.” Monthly Weather Rev., 91(6), 298–301.
8.
Chang, T. J., Kavvas, M. L., and Delleur, J. W. (1984a). “Daily precipitation modeling by discrete autoregressive moving average processes.” Wat. Resour. Res., 20(5), 565–580.
9.
Chang, T. J., Kavvas, M. L., and Delleur, J. W. (1984b). “Modeling of sequences of wet and dry days by binary discrete moving average processes.” J. Clim. Appl. Meteor., 23(9), 1367–1378.
10.
Chin, E. H. (1977). “Modeling of daily precipitation occurrence process with Markov chain.” Wat. Resour. Res., 13(6), 949–956.
11.
Chin, E. H., and Miller, J. F. (1980). “On the conditional distribution of rainfall amounts.” Monthly Weather Rev., 108(9), 1462–1464.
12.
Çinlar, E. (1975). Introduction to stochastic processes, Prentice Hall, Englewood Cliffs, N.J.
13.
Climate of the states. (1974). Water Information Ctr., Inc., Nat. Ocean and Atmospheric Admin., U.S. Dept. of Commerce, Port Washington, N.Y.
14.
Climatography of the United States No. 60, climates of the states. (1977). Envir. Data Service, Nat. Climatic Ctr., Nat. Ocean and Atmospheric Admin., U.S. Dept. of Commerce, Asheville, N.C.
15.
Cole, J. A., and Sherriff, J. D. F. (1972). “Some single‐ and multi‐site models of rainfall within discrete time increments.” J. Hydrol., 17(1/2), 97–113.
16.
Court, A. (1979). “Precipitation research, 1975–1978.” Rev. Geophys. Space Phys., 17(6), 1165–1175.
17.
Delleur, J. W., Tao, P. C., and Kavvas, K. L. (1976). “An evaluation of the practicality and complexity of some rainfall and runoff time series models.” Wat. Resour. Res., 12(5), 953–970.
18.
Eagleson, P. S. (1978). “Climate, soil and vegetation, 2. The distribution of annual precipitation derived from observed storm sequences.” Wat. Resour. Res., 14(5), 713–721.
19.
Feyerherm, A. M., and Bark, L. D. (1965). “Statistical methods for persistent precipitation pattern.” J. Appl. Meteor., 4(3), 320–328.
20.
Feyerherm, A. M., and Bark, L. D. (1967). “Goodness of fit of a Markov chain model for sequences of wet and dry days.” J. Appl. Meteor., 6(5), 770–773.
21.
Foufoula‐Georgiou, E., and Guttorp, P. (1986). “Compatability of continuous rainfall occurrence models with discrete rainfall observations.” Wat. Resour. Res., 22(8), 1316–1322.
22.
Foufoula‐Georgiou, E., and Lettenmaier, D. P. (1987). “A Markov renewal model for daily rainfall occurrences.” Wat. Resour. Res., 23(5), 875–884.
23.
Gabriel, K. R., and Neumann, J. (1962). “A Markov chain model for rainfall occurrence at Tel Aviv.” Royal Meteor. Soc., London, England, 88(375), 90–95.
24.
Gates, P., and Tong, H. (1976). “On Markov chain modeling to some weather data.” J. Appl. Meteor., 15(11), 1145–1151.
25.
Green, J. R. (1964). “A model for rainfall occurrence.” J. Royal Stat. Soc., London, England, 26(B), 345–353.
26.
Green, J. R. (1965). “Two probability models for sequences of wet and dry days.” Monthly Weather Rev., 93(3), 155–156.
27.
Green, J. R. (1970). “A generalized probability model for sequences of wet and dry days.” Monthly Weather Rev., 98(3), 238–241.
28.
Greenwood, J. A., and Durand, D. (1960). “Aids for fitting the gamma distribution by maximum likelihood.” Technometrics, 2(1), 55–56.
29.
Gupta, V. K., and Duckstein, L. (1975). “A stochastic analysis of extreme droughts.” Wat. Resour. Res., 12(2), 221–228.
30.
Guzmán, A. G., and Torrez, W. C. (1985). “Daily rainfall probabilities: conditional upon prior occurrence and amount of rain.” J. Clim. Appl. Meteor., 24(10), 1009–1014.
31.
Haan, C. T., Allen, D. M., and Street, J. O. (1976). “A Markov chain model of daily rainfall.” Wat. Resour. Res., 12(3), 443–449.
32.
Haith, D. A., Tubbs, L. J., and Pickering, N. B. (1984). Simulation of pollution by soil erosion and soil nutrient loss. Simulation monograph, Ctr. for Agric. Publishing and Documentation (Pudoc), Wageningen, The Netherlands.
33.
Hershfield, D. J. (1970). “A comparison of conditional and unconditional probabilities for wet‐ and dry‐day sequences.” J. Appl. Meteor., 9(5), 825–827.
34.
Hipel, K. W., McCloud, A. I., and Lennox, W. C. (1977). “Advances in Box‐Jenkins modeling, 1. Model construction.” Wat. Resour. Res., 13(3), 567–575.
35.
Hopkins, J. W., and Robillard, P. (1964). “Some statistics of daily rainfall occurrence for the Canadian prairie provinces.” J. Appl. Meteor., 3(5), 600–602.
36.
Jones, J. W., Colwick, R. F., and Threadgill, E. D. (1972). “A simulated environmental model for temperature, evaporation, and soil moisture.” Trans., American Society of Agricultural Engineers, 15(2), 366–372.
37.
Katz, R. W. (1974). “Computing probabilities associated with the Markov chain model for precipitation.” J. Appl. Meteor., 13(8), 953–954.
38.
Katz, R. W. (1977a). “Precipitation as a chain dependent process.” J. Appl. Meteor., 16(7), 671–676.
39.
Katz, R. W. (1977b). “An application of chain‐dependent processes to meteorology.” J. Appl. Prob., 14(3), 598–603.
40.
Katz, R. W. (1979). “Parsimony in modeling daily precipitation.” Wat. Resour. Res., 15(6), 1628–1630.
41.
Kavvas, M. L., and Delleur, J. W. (1981). “A stochastic cluster model for daily rainfall sequences.” Wat. Resour. Res., 17(4), 1151–1160.
42.
Khanal, N. N., and Hamrick, R. L. (1974). “A stochastic model for daily rainfall data synthesis.” USDA Misc. Publ. No. 1275, Proceedings of the Symposium of Statistical Hydrology, U.S. Dept. of Agric., 197–210.
43.
LeCam, L. (1961). “A stochastic description of precipitation.” 4th Berkley Symp. on Math., Statistics and Probability, J. Neyman, ed., Univ. of California, Berkley, Calif., 3, 165–186.
44.
Larsen, G. A., and Pense, R. B. (1982). “Stochastic simulation of climatic data for agronomic models.” Agron. J., 74(3), 510–514.
45.
Lowry, W. P., and Guthrie, D. (1968). “Markov chains of order greater than one.” Monthly Weather Rev., 96(11), 798–801.
46.
Meilke, P. W., Jr., and Johnson, E. S. (1974). “Some generalized beta distributions of the second kind having desirable application features in hydrology and meteorology.” Wat. Resour. Res., 10(2), 223–236.
47.
Mimikou, M. (1983). “Daily precipitation occurrence modelling with Markov chain of seasonal order.” J. Hydrol. Sci., 28(2), 221–232.
48.
Nguyen, V. T. V. (1984). “A stochastic description of temporal rainfall patterns.” Can. J. Civ. Engrg., 11(2), 234–238.
49.
Pickering, N. B. (1982). “Operational stochastic meteorologic models for nonpoint source pollution modeling,” thesis presented to Cornell Univ., Ithaca, N.Y., in partial fulfillment of the requirements for the degree of Master of Science.
50.
Raudkivi, A. J., and Lawgun, N. (1972). “Generation of serially correlated nonnomally distributed rainfall durations.” Wat. Resour. Res., 8(2), 398–409.
51.
Richardson, C. W. (1981). “Stochastic generation of daily precipitation, temperature, and solar radiation.” Wat. Resour. Res., 17(1), 182–190.
52.
Roldán, J., and Woolhiser, D. A. (1982). “Stochastic daily precipitation models 1. A comparison of occurrence processes.” Wat. Resour. Res., 18(5), 1451–1468.
53.
Selvalingham, S., and Muira, M. (1978). “Stochastic modeling of monthly and daily rainfall.” Wat. Resour. Bull., 14(5), 1105–1120.
54.
Skees, P. M., and Shenton, L. R. (1974). “Comments on the statistical distribution of rainfall per period under various transformations.” USDA Misc. Publ. No. 1275, Proc. of the Symposium on Statistical Hydrology, U.S. Dept. of Agric., 172–196.
55.
Smith, J. A., and Carr, A. F. (1983). “A point process model of summer season rainfall occurrences.” Wat. Resour. Res., 19(1), 95–103.
56.
Smith, E. R., and Schrieber, H. A. (1973). “Point processes of seasonal thunderstorm rainfall 1. Distribution of rainfall events.” Wat. Resour. Res., 9(4), 871–884.
57.
Srikanthan, R., and McMahon, T. A. (1983). “Stochastic simulation of daily rainfall for Australian stations.” Trans., American Society of Agricultural Engineers, 26(3), 754–759 and 766.
58.
Strommen, N. D., and Horsfield, J. E. (1969). “Monthly precipitation probabilities by climatic divisions.” USDA Misc. Publ. No. 1160, U.S. Dept. of Agric., Washington, D.C.
59.
Thom, H. C. S. (1958). “A note on the gamma distribution.” Mon. Wea. Rev., 86(4), 117–122.
60.
Todorovic, P., and Woolhiser, D. (1974). “Stochastic model of daily rainfall.” USDA Misc. Publ. No. 1275, Proc. of the Symposium on Statistical Hydrology, U.S. Dept. of Agric., 232–246.
61.
Todorovic, P., and Yevjevich, V. (1969). “Stochastic processes of precipitation.” Hydrol. Pap. No. 35, Colorado State Univ., Fort Collins, Colo.
62.
Tong, H. (1975). “Determination of the order of a Markov chain by Akaike's information criterion.” J. Appl. Prob., 12(3), 488–497.
63.
Tubbs, L. J., and Haith, D. A. (1981). “Simulation model for agricultural nonpointsource pollution.” J. Wat. Contr. Fed., 53(9), 1425–1433.
64.
Waymire, E., and Gupta, V. K. (1981a). “The mathematical structure of rainfall representations, 1. A review of the stochastic rainfall models.” Wat. Resour. Res., 17(5), 1261–1271.
65.
Waymire, E., and Gupta, V. K. (1981b). “The mathematical structure of rainfall representations, 2. A review of the theory of point processes.” Wat. Resour. Res., 17(5), 1273–1286.
66.
Waymire, E., and Gupta, V. K. (1981c). “The mathematical structure of rainfall representations, 3. Some applications of the point process theory to rainfall processes.” Wat. Resour. Res., 17(5), 1287–1294.
67.
Weiss, L. L. (1964). “Sequences of wet and dry days described by a Markov chain probability model.” Monthly Weather Rev., 92(4), 169–176.
68.
Wiser, E. H. (1965). “Modified Markov probability models of sequences of precipitation events.” Monthly Weather Rev., 93(8), 511–516.
69.
Wiser, E. H. (1966). “Monte Carlo method applied to precipitation‐frequency analyses.” Trans., American Society of Agricultural Engineers, 9(4), 538–540 and 542.
70.
Woolhiser, D. A., and Roldán, J. (1982). “Stochastic daily precipitation models 2. A comparison of distributions of amounts.” Wat. Resour. Res., 18(5), 1461–1468.
71.
Woolhiser, D. A., and Pegram, G. G. S. (1979). “Maximum likelihood estimation of Fourier coefficients to describe seasonal variations of parameters in stochastic daily precipitation models.” J. Appl. Meteor., 18(1), 34–42.
72.
Woolhiser, D. A., Rovey, E., and Todorovic, P. (1973). “Temporal and spatial variation of parameters for the distribution of n‐day precipitation.” Floods and droughts, E. F. Shulz, V. A. Koelzer, and K. Mahmood, eds., Water Resources Publications, Fort Collins, Colo., 605–614.
73.
Yevjevich, V. (1972). “Structural analyses of hydrologic time series.” Hydrol. Pap. No. 56, Colorado State Univ., Fort Collins, Colo.
74.
Yevjevich, V., and Dyer, T. G. J. (1983). “Basic structure of daily precipitation series.” J. Hydrol., 64(1/4), 49–67.

Information & Authors

Information

Published In

Go to Journal of Irrigation and Drainage Engineering
Journal of Irrigation and Drainage Engineering
Volume 114Issue 4November 1988
Pages: 674 - 690

History

Published online: Nov 1, 1988
Published in print: Nov 1988

Permissions

Request permissions for this article.

Authors

Affiliations

Nigel B. Pickering
Grad. Student, Dept. of Agric. Engrg., Cornell Univ., Ithaca, NY 14853
Jery R. Stedinger, Member, ASCE
Assoc. Prof., Dept. Envir. Engr., Cornell University, Ithaca, NY 14853
Douglas A. Haith, Member, ASCE
Prof., Dept. Agr. Engr., Cornell University, Ithaca, NY 14853

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share