Journal of Resources and Ecology ›› 2022, Vol. 13 ›› Issue (2): 210-219.DOI: 10.5814/j.issn.1674-764x.2022.02.004
• Ecosystem and Climate Change • Previous Articles Next Articles
Nurilign SHIBABAW(), Tesfahun BERHANE(
), Tesfaye KEBEDE, Assaye WALELIGN
Received:
2021-02-10
Accepted:
2021-06-18
Online:
2022-03-30
Published:
2022-03-09
Contact:
Tesfahun BERHANE
About author:
Nurilign SHIBABAW, E-mail: nuriligns@yahoo.com
Nurilign SHIBABAW, Tesfahun BERHANE, Tesfaye KEBEDE, Assaye WALELIGN. Spatio-temporal Rainfall Distribution and Markov Chain Analogue Year Stochastic Daily Rainfall Model in Ethiopia[J]. Journal of Resources and Ecology, 2022, 13(2): 210-219.
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Fig. 2 Seasonal distribution of rainfall Note: (a) Northwest part; (b) Central and Northeastern part; (c) Southwest section; (d) South and Southeast part of Ethiopia.
Coefficient | | | | | |
---|---|---|---|---|---|
Addis Ababa | 2.837 | -0.758 | 1.575 | -3.094 | 0.252 |
Gonder | 3.189 | -1.888 | 1.569 | -4.068 | 1.299 |
Jinka | 3.667 | -0.124 | 1.228 | -0.803 | 1.451 |
Table 1 Coefficients of ψt1
Coefficient | | | | | |
---|---|---|---|---|---|
Addis Ababa | 2.837 | -0.758 | 1.575 | -3.094 | 0.252 |
Gonder | 3.189 | -1.888 | 1.569 | -4.068 | 1.299 |
Jinka | 3.667 | -0.124 | 1.228 | -0.803 | 1.451 |
Coefficient | | | | | | | | | |
---|---|---|---|---|---|---|---|---|---|
Addis Ababa | 2.837 | -0.756 | 1.575 | -0.957 | 0.218 | -3.094 | 0.252 | 0.419 | -0.263 |
Gonder | 3.189 | -1.888 | 0.570 | -0.958 | 0.499 | -4.068 | 1.299 | 0.272 | -0.324 |
Jinka | 3.667 | -1.228 | 0.631 | -0.957 | 0.803 | -1.451 | 0.184 | 0.116 | -0.102 |
Table 2 Coefficients of ψt2
Coefficient | | | | | | | | | |
---|---|---|---|---|---|---|---|---|---|
Addis Ababa | 2.837 | -0.756 | 1.575 | -0.957 | 0.218 | -3.094 | 0.252 | 0.419 | -0.263 |
Gonder | 3.189 | -1.888 | 0.570 | -0.958 | 0.499 | -4.068 | 1.299 | 0.272 | -0.324 |
Jinka | 3.667 | -1.228 | 0.631 | -0.957 | 0.803 | -1.451 | 0.184 | 0.116 | -0.102 |
Models | Observed value | Simulated value | |||||||
---|---|---|---|---|---|---|---|---|---|
MCAYGM | AE | MCAYWBM | AE | MCAYMEM | AE | MCAYLNM | AE | ||
Jan | 0.3609 | 0.3004 | 0.0605 | 0.2997 | 0.0612 | 0.3626 | 0.0017 | 0.3248 | 0.0361 |
Feb | 0.9491 | 0.9895 | 0.0404 | 0.9911 | 0.0421 | 1.0108 | 0.0617 | 1.1309 | 0.1818 |
Mar | 1.8816 | 1.7796 | 0.1020 | 1.7977 | 0.0839 | 1.7734 | 0.1082 | 1.9605 | 0.0789 |
Apr | 3.0397 | 3.1513 | 0.1115 | 3.1702 | 0.1305 | 3.1410 | 0.1013 | 3.4277 | 0.3880 |
May | 2.5981 | 2.5434 | 0.0547 | 2.5509 | 0.0472 | 2.4613 | 0.1368 | 2.6987 | 0.1006 |
Jun | 4.0070 | 4.1037 | 0.0967 | 4.1209 | 0.1140 | 4.0833 | 0.0763 | 4.4320 | 0.4250 |
Jul | 7.3475 | 7.4031 | 0.0556 | 7.3888 | 0.0413 | 7.3311 | 0.0236 | 8.3706 | 1.0231 |
Aug | 7.9279 | 8.0064 | 0.0785 | 7.9711 | 0.0433 | 7.9961 | 0.0682 | 9.0812 | 1.1533 |
Sep | 4.3583 | 4.2749 | 0.0835 | 4.2702 | 0.0881 | 4.2748 | 0.0836 | 4.7219 | 0.3635 |
Oct | 1.0229 | 1.0009 | 0.0220 | 1.0104 | 0.0125 | 1.0180 | 0.0049 | 1.1613 | 0.1384 |
Nov | 0.1404 | 0.1317 | 0.0087 | 0.1302 | 0.0102 | 0.1640 | 0.0236 | 0.1330 | 0.0074 |
Dec | 0.2305 | 0.2595 | 0.0290 | 0.2642 | 0.0338 | 0.3150 | 0.0845 | 0.3072 | 0.0767 |
Table 3 Average daily rainfall for Addis Ababa weather station in each of the four models and their corresponding absolute error (AE)
Models | Observed value | Simulated value | |||||||
---|---|---|---|---|---|---|---|---|---|
MCAYGM | AE | MCAYWBM | AE | MCAYMEM | AE | MCAYLNM | AE | ||
Jan | 0.3609 | 0.3004 | 0.0605 | 0.2997 | 0.0612 | 0.3626 | 0.0017 | 0.3248 | 0.0361 |
Feb | 0.9491 | 0.9895 | 0.0404 | 0.9911 | 0.0421 | 1.0108 | 0.0617 | 1.1309 | 0.1818 |
Mar | 1.8816 | 1.7796 | 0.1020 | 1.7977 | 0.0839 | 1.7734 | 0.1082 | 1.9605 | 0.0789 |
Apr | 3.0397 | 3.1513 | 0.1115 | 3.1702 | 0.1305 | 3.1410 | 0.1013 | 3.4277 | 0.3880 |
May | 2.5981 | 2.5434 | 0.0547 | 2.5509 | 0.0472 | 2.4613 | 0.1368 | 2.6987 | 0.1006 |
Jun | 4.0070 | 4.1037 | 0.0967 | 4.1209 | 0.1140 | 4.0833 | 0.0763 | 4.4320 | 0.4250 |
Jul | 7.3475 | 7.4031 | 0.0556 | 7.3888 | 0.0413 | 7.3311 | 0.0236 | 8.3706 | 1.0231 |
Aug | 7.9279 | 8.0064 | 0.0785 | 7.9711 | 0.0433 | 7.9961 | 0.0682 | 9.0812 | 1.1533 |
Sep | 4.3583 | 4.2749 | 0.0835 | 4.2702 | 0.0881 | 4.2748 | 0.0836 | 4.7219 | 0.3635 |
Oct | 1.0229 | 1.0009 | 0.0220 | 1.0104 | 0.0125 | 1.0180 | 0.0049 | 1.1613 | 0.1384 |
Nov | 0.1404 | 0.1317 | 0.0087 | 0.1302 | 0.0102 | 0.1640 | 0.0236 | 0.1330 | 0.0074 |
Dec | 0.2305 | 0.2595 | 0.0290 | 0.2642 | 0.0338 | 0.3150 | 0.0845 | 0.3072 | 0.0767 |
Month | Observed value | Simulated value | |||||||
---|---|---|---|---|---|---|---|---|---|
MCAYGM | AE | MCAYWBM | AE | MCAYMEM | AE | MCAYLNM | AE | ||
Jan | 0.1145 | 0.1291 | 0.0147 | 0.1280 | 0.0135 | 0.1983 | 0.0839 | 0.1290 | 0.0145 |
Feb | 0.1314 | 0.1928 | 0.0614 | 0.1933 | 0.0619 | 0.2208 | 0.0894 | 0.2090 | 0.0776 |
Mar | 0.5148 | 0.4539 | 0.0609 | 0.4406 | 0.0742 | 0.4536 | 0.0612 | 0.4231 | 0.0917 |
Apr | 1.0980 | 1.0106 | 0.0874 | 1.0029 | 0.0951 | 0.4536 | 0.0612 | 1.0652 | 0.0328 |
May | 2.7638 | 2.7560 | 0.0079 | 2.7211 | 0.0427 | 2.7458 | 0.0181 | 2.8964 | 0.1326 |
Jun | 5.8020 | 5.9059 | 0.1039 | 5.9128 | 0.1109 | 5.9047 | 0.1028 | 6.6651 | 0.8632 |
Jul | 10.0538 | 10.2464 | 0.1925 | 10.2682 | 0.2144 | 10.2440 | 0.1902 | 11.6851 | 1.6312 |
Aug | 9.9574 | 9.9019 | 0.0555 | 9.9273 | 0.0301 | 9.9106 | 0.0468 | 11.3244 | 1.3670 |
Sep | 3.9097 | 3.9524 | 0.0428 | 3.9767 | 0.0670 | 3.9709 | 0.0613 | 4.4416 | 0.5319 |
Oct | 2.5963 | 2.5378 | 0.0585 | 0.6640 | 0.0002 | 2.5196 | 0.0767 | 2.9164 | 0.3200 |
Nov | 0.6643 | 0.6685 | 0.0042 | 2.5041 | 0.0922 | 0.6191 | 0.0452 | 0.7241 | 0.0598 |
Dec | 0.3216 | 0.2899 | 0.0317 | 0.2865 | 0.0351 | 0.2847 | 0.0369 | 0.3007 | 0.0209 |
Table 4 Average daily rainfall for Gonder weather station in each of the four models and their corresponding absolute error (AE)
Month | Observed value | Simulated value | |||||||
---|---|---|---|---|---|---|---|---|---|
MCAYGM | AE | MCAYWBM | AE | MCAYMEM | AE | MCAYLNM | AE | ||
Jan | 0.1145 | 0.1291 | 0.0147 | 0.1280 | 0.0135 | 0.1983 | 0.0839 | 0.1290 | 0.0145 |
Feb | 0.1314 | 0.1928 | 0.0614 | 0.1933 | 0.0619 | 0.2208 | 0.0894 | 0.2090 | 0.0776 |
Mar | 0.5148 | 0.4539 | 0.0609 | 0.4406 | 0.0742 | 0.4536 | 0.0612 | 0.4231 | 0.0917 |
Apr | 1.0980 | 1.0106 | 0.0874 | 1.0029 | 0.0951 | 0.4536 | 0.0612 | 1.0652 | 0.0328 |
May | 2.7638 | 2.7560 | 0.0079 | 2.7211 | 0.0427 | 2.7458 | 0.0181 | 2.8964 | 0.1326 |
Jun | 5.8020 | 5.9059 | 0.1039 | 5.9128 | 0.1109 | 5.9047 | 0.1028 | 6.6651 | 0.8632 |
Jul | 10.0538 | 10.2464 | 0.1925 | 10.2682 | 0.2144 | 10.2440 | 0.1902 | 11.6851 | 1.6312 |
Aug | 9.9574 | 9.9019 | 0.0555 | 9.9273 | 0.0301 | 9.9106 | 0.0468 | 11.3244 | 1.3670 |
Sep | 3.9097 | 3.9524 | 0.0428 | 3.9767 | 0.0670 | 3.9709 | 0.0613 | 4.4416 | 0.5319 |
Oct | 2.5963 | 2.5378 | 0.0585 | 0.6640 | 0.0002 | 2.5196 | 0.0767 | 2.9164 | 0.3200 |
Nov | 0.6643 | 0.6685 | 0.0042 | 2.5041 | 0.0922 | 0.6191 | 0.0452 | 0.7241 | 0.0598 |
Dec | 0.3216 | 0.2899 | 0.0317 | 0.2865 | 0.0351 | 0.2847 | 0.0369 | 0.3007 | 0.0209 |
Month | Observed value | Simulated value | |||||||
---|---|---|---|---|---|---|---|---|---|
MCAYGM | AE | MCAYWBM | AE | MCAYMEM | AE | MCAYLNM | AE | ||
Jan | 1.5350 | 1.4163 | 0.1187 | 1.4022 | 0.1328 | 1.4539 | 0.0811 | 1.5687 | 0.0337 |
Feb | 1.8078 | 1.7229 | 0.0849 | 1.7280 | 0.0798 | 1.7364 | 0.0714 | 1.8371 | 0.0293 |
Mar | 3.6064 | 3.6901 | 0.0838 | 3.6763 | 0.0700 | 3.6225 | 0.0162 | 3.9716 | 0.3653 |
Apr | 6.5297 | 6.4680 | 0.0639 | 6.4538 | 0.0759 | 6.4622 | 0.0674 | 7.1270 | 0.5973 |
May | 5.1542 | 5.2192 | 0.0650 | 5.2068 | 0.0527 | 5.2274 | 0.0732 | 5.8169 | 0.6627 |
Jun | 3.5117 | 3.5050 | 0.0267 | 3.4826 | 0.0491 | 3.4727 | 0.0591 | 3.9712 | 0.4395 |
Jul | 3.1684 | 3.3750 | 0.2066 | 3.3607 | 0.1923 | 3.2549 | 0.0864 | 3.7192 | 0.5508 |
Aug | 3.1061 | 3.0507 | 0.0554 | 3.0345 | 0.0716 | 3.1035 | 0.0025 | 3.2733 | 0.1672 |
Sep | 3.9003 | 3.9752 | 0.0749 | 3.9697 | 0.0694 | 4.0186 | 0.1183 | 4.4518 | 0.5515 |
Oct | 5.4380 | 5.5533 | 0.1153 | 5.5095 | 0.0714 | 5.5651 | 0.1271 | 6.0701 | 0.6568 |
Nov | 3.8471 | 3.9831 | 0.1360 | 3.9747 | 0.1276 | 3.9436 | 0.0966 | 4.5039 | 0.6568 |
Dec | 2.2964 | 2.2254 | 0.0710 | 2.2134 | 0.0830 | 2.2365 | 0.0599 | 2.4757 | 0.1793 |
Table 5 Average daily rainfall for Jinka weather station in each of the four models and their corresponding absolute error (AE)
Month | Observed value | Simulated value | |||||||
---|---|---|---|---|---|---|---|---|---|
MCAYGM | AE | MCAYWBM | AE | MCAYMEM | AE | MCAYLNM | AE | ||
Jan | 1.5350 | 1.4163 | 0.1187 | 1.4022 | 0.1328 | 1.4539 | 0.0811 | 1.5687 | 0.0337 |
Feb | 1.8078 | 1.7229 | 0.0849 | 1.7280 | 0.0798 | 1.7364 | 0.0714 | 1.8371 | 0.0293 |
Mar | 3.6064 | 3.6901 | 0.0838 | 3.6763 | 0.0700 | 3.6225 | 0.0162 | 3.9716 | 0.3653 |
Apr | 6.5297 | 6.4680 | 0.0639 | 6.4538 | 0.0759 | 6.4622 | 0.0674 | 7.1270 | 0.5973 |
May | 5.1542 | 5.2192 | 0.0650 | 5.2068 | 0.0527 | 5.2274 | 0.0732 | 5.8169 | 0.6627 |
Jun | 3.5117 | 3.5050 | 0.0267 | 3.4826 | 0.0491 | 3.4727 | 0.0591 | 3.9712 | 0.4395 |
Jul | 3.1684 | 3.3750 | 0.2066 | 3.3607 | 0.1923 | 3.2549 | 0.0864 | 3.7192 | 0.5508 |
Aug | 3.1061 | 3.0507 | 0.0554 | 3.0345 | 0.0716 | 3.1035 | 0.0025 | 3.2733 | 0.1672 |
Sep | 3.9003 | 3.9752 | 0.0749 | 3.9697 | 0.0694 | 4.0186 | 0.1183 | 4.4518 | 0.5515 |
Oct | 5.4380 | 5.5533 | 0.1153 | 5.5095 | 0.0714 | 5.5651 | 0.1271 | 6.0701 | 0.6568 |
Nov | 3.8471 | 3.9831 | 0.1360 | 3.9747 | 0.1276 | 3.9436 | 0.0966 | 4.5039 | 0.6568 |
Dec | 2.2964 | 2.2254 | 0.0710 | 2.2134 | 0.0830 | 2.2365 | 0.0599 | 2.4757 | 0.1793 |
Station | Observed | Simulated | |||
---|---|---|---|---|---|
MCAYGM | MCAYWBM | MCAYWBM | MCAYLNM | ||
Addis Ababa | 1035.4 | 1038.3 | 1037.6 | 1038.4 | 1154.1 |
Gonder | 1163.9 | 1167.3 | 1166.7 | 1166.3 | 1312.7 |
Jinka | 1338.3 | 1346.5 | 1341.3 | 1343.9 | 1486.8 |
Table 6 Mean annual rainfall for Addis Ababa, Gonder and Jinka (mm)
Station | Observed | Simulated | |||
---|---|---|---|---|---|
MCAYGM | MCAYWBM | MCAYWBM | MCAYLNM | ||
Addis Ababa | 1035.4 | 1038.3 | 1037.6 | 1038.4 | 1154.1 |
Gonder | 1163.9 | 1167.3 | 1166.7 | 1166.3 | 1312.7 |
Jinka | 1338.3 | 1346.5 | 1341.3 | 1343.9 | 1486.8 |
Model | Addis Ababa | Gonder | Jinka |
---|---|---|---|
MC | 10.51 | 10.35 | 10.31 |
MCAY | 2.22 | 2.33 | 1.99 |
Table 7 Mean absolute percentage error (MAPE) in describing the average number of wet days for Addis Ababa, Gonder and Jinka, Ethiopia (Unit: %)
Model | Addis Ababa | Gonder | Jinka |
---|---|---|---|
MC | 10.51 | 10.35 | 10.31 |
MCAY | 2.22 | 2.33 | 1.99 |
[1] |
Akaike H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6): 716-723.
DOI URL |
[2] |
Berhane T, Shibabaw N, Awgichew G, et al. 2020. Option pricing of weather derivatives based on a stochastic daily rainfall model with analogue year component. Heliyon, 6(1): e03212. DOI: 10.1016/j.heliyon.2020.e03212.
DOI URL |
[3] |
Berhanu B, Melesse A M, Seleshi Y. 2013. GIS-based hydrological zones and soil geo-database of Ethiopia. CATENA, 104: 21-31.
DOI URL |
[4] |
Berhanu B, Seleshi Y, Melesse A M. 2014. Surface water and groundwater resources of Ethiopia: Potentials and challenges of water resources development. In: Nile River Basin. Springer. DOI: 10.1007/978-3-319-02 720-3_6.
DOI |
[5] | Bewket W. 2009. Rainfall variability and crop production in Ethiopia: Case study in the Amhara region. In: Proceedings of the 16th International Conference of Ethiopian Studies. Norwegian University of Science and Technology, Trondheim, Norway, 3: 823-836. |
[6] |
Block P J, Souza Filho F A, Sun L, et al. 2009. A streamflow forecasting framework using multiple climate and hydrological Models 1: JAWRA. Journal of the American Water Resources Association, 45(4): 828-843.
DOI URL |
[7] |
Caskey J E. 1963. A Markov chain model for the probability of precipitation occurrence in intervals of various length. Monthly Weather Review, 91(6): 298-301.
DOI URL |
[8] |
Devereux S. 2001. Livelihood insecurity and social protection: A re-emerging issue in rural development. Development Policy Review, 19(4): 507-519.
DOI URL |
[9] |
Di Falco S, Yesuf M, Kohlin G, et al. 2012. Estimating the impact of climate change on agriculture in low-income countries: Household level evidence from the Nile basin, Ethiopia. Environmental and Resource Economics, 52(4): 457-478.
DOI URL |
[10] |
Diro G T, Grimes D I F, Black E, et al. 2009. Evaluation of reanalysis rainfall estimates over Ethiopia. International Journal of Climatology, 29(1): 67-78.
DOI URL |
[11] | Diro G T, Toniazzo T, Shaffrey L. 2011. Ethiopian rainfall in climate models. In: African climate and climate change, Dordrecht, Netherlands: Springer, 51-69. |
[12] | Gezie M. 2019. Farmer’s response to climate change and variability in Ethiopia: A review. Cogent Food and Agriculture, 5(1): 1-13. |
[13] | Goncu A. 2011. Modeling and pricing precipitation-based weather derivatives. Financial Mathematics and Applications, 1(1): 9-18. |
[14] |
Groisman P Y, Karl T R, Easterling D R, et al. 1999. Changes in the probability of heavy precipitation: Important indicators of climatic change. Climatic Change, 42(1): 243-283.
DOI URL |
[15] |
Guida D, Longobardi A, Villani P. 2006. Hydrological modelling for river basin management in a highly hydro-geological conditioned environment. WIT Transactions on Ecology and the Environment, 89. DOI: 10.2495/GEO060291.
DOI |
[16] | Hagosa F, Makombe G, Namara R E, et al. 2011. Importance of irrigated agriculture to the Ethiopian economy: Capturing the direct net benefits of irrigation. Ethiopian Journal of Development Research, 32(1): 5-53. |
[17] |
Husak G J, Michaelsen J, Funk C. 2007. Use of the gamma distribution to represent monthly rainfall in Africa for drought monitoring applications. International Journal of Climatology, 27(7): 935-944.
DOI URL |
[18] |
Ines A V, Hansen J W. 2006. Bias correction of daily GCM rainfall for crop simulation studies. Agricultural and Forest Meteorology, 138(1-4): 44-53.
DOI URL |
[19] |
Kang S Z, Gu B J, Du T S, et al. 2003. Crop coefficient and ratio of transpiration to evapotranspiration of winter wheat and maize in a semi-humid region. Agricultural Water Management, 59(3): 239-254.
DOI URL |
[20] | Kannan S K, Farook J A. 2015. Stochastic simulation of precipitation using Markov chain-mixed exponential model. Applied Mathematical Sciences, 65(9): 3205-3212. |
[21] |
Katz R W. 1981. On some criteria for estimating the order of a Markov chain. Technometrics, 23(3): 243-249.
DOI URL |
[22] |
Katz R W. 1999. Extreme value theory for precipitation: sensitivity analysis for climate change. Advances in Water Resources, 23(2): 133-139.
DOI URL |
[23] |
Kottegoda N, Natale L, Raiteri E. 2004. Some considerations of periodicity and persistence in daily rainfalls. Journal of hydrology, 296(1-4): 23-37.
DOI URL |
[24] |
Makombe G, Kelemework D, Aredo D. 2007. A comparative analysis of rain fed and irrigated agricultural production in Ethiopia. Irrigation and Drainage Systems, 21(1): 35-44.
DOI URL |
[25] | McSweeney CMN LG. 2012. UNDP climate change country profiles Ethiopia. http://country-profiles.geog.ox.ac.uk. Accessed 4 August 2013. |
[26] | Mearns R, Norton A. 2009. The social dimensions of climate change:Equity and vulnerability in a warming world. Washington DC, USA: The World Bank. |
[27] | NMA. 1996. Climatic and agro climatic resources of Ethiopia. National Meteorological Services Agency of Ethiopia. Meteorological Research Report Series, 1(1): 1-137. |
[28] |
Odening M, Musshoff O, Xu W. 2007. Analysis of rainfall derivatives using daily precipitation models: Opportunities and pitfalls. Agricultural Finance Review, 67(1): 135-156.
DOI URL |
[29] |
Papalexiou S, Koutsoyiannis D, Makropoulos C. 2012. How extreme is extreme? An assessment of daily rainfall distribution tails. Hydrology and Earth System Sciences Discussions, 9(5). DOI: 10.5194/hessd-9-5757-2012.
DOI |
[30] |
Papalexiou S M, Koutsoyiannis D, Makropoulos C. 2013. How extreme is extreme? An assessment of daily rainfall distribution tails. Hydrology and Earth System Sciences, 17(2): 851-862.
DOI URL |
[31] |
Papalexiou S M, Koutsoyiannis D. 2016. A global survey on the seasonal variation of the marginal distribution of daily precipitation. Advances in Water Resources, 94: 131-145.
DOI URL |
[32] |
Piani C, Haerter J O, Coppola E. 2010. Statistical bias correction for daily precipitation in regional climate models over Europe. Theoretical and Applied Climatology, 99(1-2): 187-192.
DOI URL |
[33] |
Piantadosi J, Boland J, Howlett P. 2009. Generating synthetic rainfall on various timescales daily, monthly and yearly. Environmental Modeling and Assessment, 14(4): 431-438.
DOI URL |
[34] |
Rahman M S. 2000. A rainfall simulation model for agricultural development in Bangladesh. Discrete Dynamics in Nature and Society, 5(1): 1-7.
DOI URL |
[35] |
Richardson C W. 1981. Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resources Research, 17(1): 182-190.
DOI URL |
[36] |
Rosenberg K, Boland J, Howlett P. 2004. Simulation of monthly rainfall totals. ANZIAM Journal, 46: 85-104.
DOI URL |
[37] | Stern R D, Coe R. 1984. A model fitting analysis of daily rainfall data. Journal of the Royal Statistical Society: Series A (General), 147(1): 1-18. |
[38] | Schwarz G. 1978. Estimating the dimension of a model. Annals of Statistics, 6(2): 461-464. |
[39] |
Stowasser M. 2011. Modelling rain risk: A multi-order Markov chain model approach. The Journal of Risk Finance, 13(1): 45-60.
DOI URL |
[40] |
Todorovic P, Woolhiser D A. 1975. A stochastic model of n-day precipitation. Journal of Applied Meteorology, 14(1): 17-24.
DOI URL |
[41] | Udomboso C, Chubwu A, Nja M. 2010. The use of gamma and Weibull distributions in modeling rainfall data in Nigeria (a comparative analysis). Journal of Science Research, 9: 69-73. |
[42] |
Weiss L L. 1964. Sequences of wet or dry days described by a Markov chain probability model. Monthly Weather Review, 92(4): 169-176.
DOI URL |
[43] |
Wilby R, Greenfield B, Glenny C. 1994. A coupled synoptic-hydrological model for climate change impact assessment. Journal of Hydrology, 153(1-4): 265-290.
DOI URL |
[44] |
Wilks D S. 1990. Maximum likelihood estimation for the gamma distribution using data containing zeros. Journal of Climate, 3(12): 1495-1501.
DOI URL |
[45] | Wilks D S. 2011. Statistical methods in the atmospheric sciences. San Diego, USA: Academic Press. |
[46] | Wilks D S, Wilby R L. 1999. The weather generation game: A review of stochastic weather models. Progress in Physical Geography: Earth and Environment, 23(3): 329-357. |
[47] |
Woolhiser D A, Pegram G. 1979. Maximum likelihood estimation of Fourier coefficients to describe seasonal variations of parameters in stochastic daily precipitation models. Journal of Applied Meteorology, 18(1): 34-42.
DOI URL |
[48] |
Woolhiser D A, Roldan J. 1982. Stochastic daily precipitation models: 1. A comparison of occurrence processes. Water Resources Research, 18(5): 1451-1459.
DOI URL |
[49] |
Ye L, Hanson L S, Ding P Q, et al. 2018. The probability distribution of daily precipitation at the point and catchment scales in the United States. Hydrology and Earth System Sciences, 22(12): 6519-6531.
DOI URL |
[50] |
Zeleke T, Giorgi F, Tsidu G M, et al. 2013. Spatial and temporal variability of summer rainfall over Ethiopia from observations and a regional climate model experiment. Theoretical and Applied Climatology, 111(3-4): 665-681.
DOI URL |
[51] | Zolina O, Simmer C, Kapala A, et al. 2008. Seasonally dependent changes of precipitation extremes over Germany since 1950 from a very dense observational network. Journal of Geophysical Research: Atmospheres, 113(6): 1-17. |
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