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Module 5: uncertainty and risk, seasonal analysis

This notebook follows the fifth day of a DSSAT training course. A single season says little about a management choice: the next season’s weather is unknown. Each exercise here runs a choice over many seasons and judges it by the whole distribution of outcomes.

  1. Seasonal analysis: the irrigation strategies of UFGA7812.SNX over 30 seasons of generated weather, with the experiment’s price and cost file.
  2. The nitrogen exercise: the economically best urea rate for maize at Kadoma, Zimbabwe, built as KADO9901.SNX exactly as the course specifies, for each of 13 seasons and as one “blanket” rate.
  3. Regional risk analysis and adoption: two millet varieties on two soils at Tillabery, Niger (NIGE1101.SNX), a price penalty for late maturity, and the variety a risk-averse farmer would choose.

Data. Seasonal/UFGA7812.SNX, Economic/UFGA7812.PRI, Weather/Climate/UFGA.CLI, the Kadoma and Tillabery weather files and the soil file from DSSAT/dssat-csm-data (BSD-3); NIGE1101.SNX from the course data (notebooks/course-data/).

engine   : C:\TEMP\dsn\dssat\dscsm048.exe
csm-data : C:\Users\benny\OneDrive\Documents\Github\dssat-csm-data @ 99c95b34

1. Seasonal analysis: irrigation strategies over 30 seasons

UFGA7812.SNX runs Bragg soybean for 30 seasons from 1978. Treatment 1 is rainfed; treatments 2 to 10 irrigate automatically when the available soil water in the top 30 cm falls to 10%, 20% … 90% of its capacity. The weather option WTHER is W: the engine generates daily weather from the monthly statistics of the climate file UFGA.CLI (the WGEN generator), so the 30 seasons are 30 samples of Gainesville’s climate, not the weather of 1978-2007.

*SIMULATION CONTROLS
@N GENERAL     NYERS NREPS START SDATE RSEED SNAME.................... SMODEL
 1 GE             30     1     S 78166  9875 Rainfed
@N OPTIONS     WATER NITRO SYMBI PHOSP POTAS DISES  CHEM  TILL   CO2
 1 OP              Y     Y     Y     N     N     N     N     Y     D
@N METHODS     WTHER INCON LIGHT EVAPO INFIL PHOTO HYDRO NSWIT MESOM MESEV MESOL
 1 ME              W     M     E     R     S     L     R     1     G     R     2
@N MANAGEMENT  PLANT IRRIG FERTI RESID HARVS
 1 MA              R     N     R     N     M
@N OUTPUTS     FNAME OVVEW SUMRY FROPT GROUT CAOUT WAOUT NIOUT MIOUT DIOUT VBOSE CHOUT OPOUT FMOPT
 1 OU              Y     N     Y     1     N     N     N   
300 seasons in 15 s
HWAM IRCM IR#M PRCM
mean std mean std mean std mean std
treatment
rainfed 2932.0 537.0 0.0 0.0 0.0 0.0 663.0 180.0
auto 10% 2987.0 467.0 8.0 12.0 0.0 1.0 667.0 179.0
auto 20% 3267.0 321.0 32.0 20.0 2.0 1.0 684.0 178.0
auto 30% 3489.0 224.0 72.0 41.0 4.0 2.0 651.0 161.0
auto 40% 3688.0 128.0 106.0 46.0 6.0 3.0 640.0 163.0
auto 50% 3780.0 104.0 144.0 47.0 9.0 3.0 637.0 161.0
auto 60% 3820.0 107.0 175.0 46.0 13.0 3.0 631.0 161.0
auto 70% 3840.0 105.0 203.0 48.0 17.0 4.0 631.0 161.0
auto 80% 3855.0 103.0 240.0 53.0 24.0 5.0 633.0 163.0
auto 90% 3854.0 103.0 295.0 51.0 35.0 6.0 633.0 163.0

From yields to money

The price file UFGA7812.PRI gives, per treatment, the soybean price as a normal distribution (mean and standard deviation, IDIS = 3) and fixed costs. Their meaning is in the engine’s ECONOMIC.CDE: GRAN grain price in $/t, BASE base production costs in $/ha, IRRI irrigation cost in $/mm, IRCO cost per irrigation application in $/ha. The gross margin of a season is

price x yield - BASE - IRRI x irrigation - IRCO x number of irrigations.

Seed costs (SCOS, $/kg) are left out: the file gives no seeding rate in kg. One price is drawn per season and used for all ten treatments, so the treatments are compared under the same prices.

      IDIS    PAR1  PAR2  PAR3
GRAN   3.0  320.00  32.0   0.0
BASE   0.0  120.00   0.0   0.0
IRRI   0.0    0.50   0.0   0.0
IRCO   0.0    0.50   0.0   0.0
SCOS   0.0    0.46   0.0   0.0
all treatments have the same prices and costs: True
treatment mean_yield sd_yield mean_irr mean_margin sd_margin p10_margin min_margin
0 rainfed 2932.233333 537.405689 0.000000 860.165100 213.526974 587.408884 495.871313
1 auto 10% 2986.900000 467.080836 8.066667 874.048685 197.324293 637.420581 585.808572
2 auto 20% 3267.433333 321.003350 32.466667 952.684211 149.660359 773.998045 690.161076
3 auto 30% 3489.133333 223.695257 71.533333 1005.287026 134.030972 854.405328 784.540699
4 auto 40% 3688.166667 127.876310 105.500000 1053.276489 117.554370 918.755106 889.340005
5 auto 50% 3779.966667 104.085669 143.966667 1062.526753 107.818962 930.276065 914.595194
6 auto 60% 3820.066667 106.792074 175.300000 1057.809445 94.459694 933.088386 919.392102
7 auto 70% 3839.866667 104.912684 202.566667 1048.825380 95.140914 916.024867 892.085503
8 auto 80% 3855.433333 102.993700 240.200000 1031.658207 98.707458 902.085533 884.375606
9 auto 90% 3853.800000 102.661614 294.600000 998.579042 97.473282 871.182682 853.959999

Comparing distributions

Two ways to compare strategies over the 30 seasons:

  • First-degree stochastic dominance: strategy A dominates B if, for every margin level, A is at least as likely as B to reach it (A’s cumulative distribution lies nowhere above B’s).
  • Risk attitude: with an exponential utility u(m) = -exp(-r m) the certainty equivalent CE = -ln(mean(exp(-r m))) / r is the sure margin a farmer with risk aversion r would accept instead of the uncertain one. r = 0 is the plain mean.
not dominated by any other strategy: ['rainfed', 'auto 10%', 'auto 30%', 'auto 40%', 'auto 50%', 'auto 60%', 'auto 70%', 'auto 80%']
r treatment CE
5 0.000 auto 50% 1062.526753
15 0.002 auto 50% 1051.896205
25 0.005 auto 50% 1037.983959
36 0.010 auto 60% 1020.550735
46 0.020 auto 60% 995.333470
56 0.050 auto 60% 960.781838 
WindowsPath('C:/Users/benny/OneDrive/Documents/Github/xdssat/docs/learn/data/module5/ufga_climate.csv')

2. The nitrogen exercise: maize at Kadoma, Zimbabwe

The course asks for the urea rate that maximizes the gross margin of rainfed maize at the Cotton Research Institute, Kadoma (Natural Region II of central Zimbabwe), first for one season, then as a “blanket” rate over all 13 seasons of measured weather (1977/78 to 1989/90). The experiment, KADO9901.SNX, is hypothetical and fully specified by the exercise:

  • cultivar MH-16 from Malawi, entered in the cultivar file as given: IB0098 MH-16 . IB0001 260.0 0.600 840.0 600.0 6.00 38.90;
  • the Millhopper fine sand IBMZ910014, measured weather of station KADO;
  • initial conditions on 7 October: previous crop maize, 10 kg/ha of roots, no nodules, 100 kg/ha of surface residue with 0.5% N, soil water at 50% of the available range, 5 kg/ha of soil N;
  • planting on 15 October, 3.7 plants/m² planted and emerged, 61 cm rows, 7 cm deep;
  • urea in two equal splits, at planting and 30 days later, incorporated to 5 cm; no irrigation;
  • simulation from 7 October, 1 year per season (part A) or 13 years (part B).

The exercise’s “5 kg/ha of soil N” is spread here as nitrate at the same concentration in every layer (no ammonium), which is a choice: the exercise does not say how XBuild divides it.

soil NO3 0.201 ppm in every layer gives 5 kg N/ha
['IB0098 MH-16                . IB0001 260.0 0.600 840.0 600.0 6.000 38.90 ']
*EXP.DETAILS: KADO7701SN KADOMA MAIZE N RATES (COURSE EXERCISE)

*GENERAL
@PEOPLE
DSSAT training exercise, built in Python
@SITE
Cotton Research Institute, Kadoma, Zimbabwe

*TREATMENTS                        -------------FACTOR LEVELS------------
@N R O C TNAME.................... CU FL SA IC MP MI MF MR MC MT ME MH SM
 1 1 0 0 UREA 0 KG N/HA             1  1  0  1  1  0  0  0  0  0  0  0  1
 2 1 0 0 UREA 20 KG N/HA            1  1  0  1  1  0  1  0  0  0  0  0  1
 3 1 0 0 UREA 40 KG N/HA            1  1  0  1  1  0  2  0  0  0  0  0  1
 4 1 0 0 UREA 60 KG N/HA            1  1  0  1  1  0  3  0  0  0  0  0  1
 5 1 0 0 UREA 80 KG N/HA            1  1  0  1  1  0  4  0  0  0  0  0  1
 6 1 0 0 UREA 100 KG N/HA           1  1  0  1  1  0  5  0  0  0  0  0  1
 7 1 0 0 UREA 120 KG N/HA           1  1  0  1  1  0  6  0  0  0  0  0  1
 8 1 0 0 UREA 140 KG N/HA           1  1  0  1  1  0  7  0  0  0  0  0  1
 9 1 0 0 UREA 160 KG N/HA           1  1  0  1  1  0  8  0  0  0  0  0  1
10 1 0 0 UREA 180 KG N/HA           1  1  0  1  1  0  9  0  0  0  0  0  1
11 1 0 0 UREA 200 KG N/HA           1  1  0  1  1  0 10  0  0  0  0  0  1
12 1 0 0 UREA 220 KG N/HA           1  1  0  1  1  0 11  0  0  0  0  0  1
13 1 0 0 UREA 240 KG N/HA           1  1  0  1  1  0 12  0  0  0  0  0  1

*CULTIVARS
@C CR INGENO CNAME
 1 MZ IB0098 MH-16


169 seasons in 12 s
rate 0 20 40 60 80 100 120 140 160 180 200 220 240
season
1977/78 782 1810 3432 4958 5314 5315 5324 5330 5339 5348 5354 5362 5366
1978/79 548 1312 2355 3504 4638 4897 4942 4920 4902 4879 4870 4873 4893
1979/80 548 1038 1567 2130 2562 3093 3775 4080 4141 4201 4213 4210 4215
1980/81 563 1075 1833 2667 3681 4366 5241 5262 5301 5366 5401 5419 5426
1981/82 666 1256 2303 3420 3666 3767 3701 3703 3710 3713 3717 3724 3729
1982/83 618 920 1328 2080 2450 2510 2320 2280 2282 2283 2270 2272 2268
1983/84 682 1570 2579 3321 3953 3872 3541 3402 3338 3300 3297 3297 3291
1984/85 673 1287 2280 3763 4569 4723 4840 4884 4901 4900 4895 4889 4880
1985/86 433 1234 2270 2544 2523 2536 2541 2545 2544 2548 2549 2544 2546
1986/87 396 936 1377 1765 2068 2112 2692 2816 2837 2842 2721 2696 2667
1987/88 807 1469 1469 1467 1468 1469 1470 1471 1471 1472 1472 1473 1473
1988/89 538 1212 1517 1644 2443 2438 2386 2225 2083 1985 1920 1909 1896
1989/90 534 638 910 1225 1292 1402 1386 1410 1466 1486 1496 1495 1476

The gross margin

The exercise’s fictitious prices, in Zimbabwean dollars: GM = Y x P - N x C - F, with Y the yield in t/ha, P = Z$ 400/t, N the amount of urea used and C = Z$ 2.0/kg, F = Z$ 750/ha of fixed costs. The exercise calls N both “the amount of urea used” and “the amount of urea N”; the notebook prices each kilogram of N at Z$ 2.0 and the page lets you change that (urea is 46% N, so Z$ 2.0 per kilogram of urea would be about Z$ 4.35 per kilogram of N).

blanket optimum: 120 kg N/ha
season rate HWAM GM PRCM
52 1977/78 80 5314 1215.6 700
66 1978/79 100 4897 1008.8 439
93 1979/80 140 4080 602.0 613
81 1980/81 120 5241 1106.4 727
69 1981/82 100 3767 556.8 301
57 1982/83 80 2450 70.0 395
58 1983/84 80 3953 671.2 371
85 1984/85 120 4840 946.0 814
47 1985/86 60 2544 147.6 718
100 1986/87 140 2816 96.4 455
23 1987/88 20 1469 -202.4 359
63 1988/89 80 2443 67.2 451
51 1989/90 60 1225 -380.0 688
rate mean_yield sd_yield mean_GM sd_GM mean_leached mean_uptake
0 0 599.0 122.0 -510.0 49.0 8.0 29.0
1 20 1212.0 304.0 -305.0 122.0 7.0 47.0
2 40 1940.0 675.0 -54.0 270.0 8.0 63.0
3 60 2653.0 1087.0 191.0 435.0 9.0 78.0
4 80 3125.0 1267.0 340.0 507.0 12.0 91.0
5 100 3269.0 1312.0 358.0 525.0 16.0 100.0
6 120 3397.0 1385.0 369.0 554.0 21.0 105.0
7 140 3410.0 1404.0 334.0 561.0 26.0 109.0
8 160 3409.0 1415.0 294.0 566.0 32.0 112.0
9 180 3409.0 1429.0 254.0 572.0 37.0 114.0
10 200 3398.0 1443.0 209.0 577.0 43.0 116.0
11 220 3397.0 1448.0 169.0 579.0 49.0 117.0
12 240 3394.0 1455.0 128.0 582.0 55.0 118.0

3. Regional risk analysis and adoption: millet in Niger

The course’s NIGE1101.SNX simulates millet at Tillabery, Niger, for 10 years of measured weather, two cultivars on two soils: a medium alfisol (IBML910083, soil type A) and a Niger sandy soil (IBML910001, soil type B). The cultivars are entered in the cultivar file as the exercise gives them:

P1 P2O P2R P5 G1 G4 PHINT GT G5
Niger 1 (NI0001) 120.0 12.00 142.0 590.0 1.00 0.60 43.00 1.0 11.0
Niger 2 (NI0002) 120.0 12.00 125.0 360.0 2.00 0.50 43.00 1.0 11.0

The region: 100 farms on soil A (2 ha each on average; 20% of these farmers do not grow millet) and 150 farms on soil B (1.8 ha each). Part B adds a heavy price penalty for late maturity, price (CFA/t) = 300 - 0.02 D² with D the days from planting to maturity, and compares the cultivars by utility = E - 0.35 V, with E the mean gross margin and V its variance.

990001 NORTH VARIETY        . IB0001 120.0 12.00 125.0 360.0  2.00  0.50 43.00  1.00  11.0
NI0001 Niger 1              . IB0001 120.0 12.00 142.0 590.0  1.00  0.60 43.00  1.00  11.0
NI0002 Niger 2              . IB0001 120.0 12.00 125.0 360.0  2.00  0.50 43.00  1.00  11.0
40 seasons in 3 s
millet area, ha: {'A': 160.0, 'B': 270.0}
soil cultivar mean_yield sd_yield mean_D mean_price E V utility
0 A Niger 1 2606.7 780.738689 104.4 81.768 214.298426 7246.129654 -2321.846953
1 A Niger 2 1412.5 446.246880 88.0 144.912 204.194460 4031.378455 -1206.787999
2 B Niger 1 1394.6 360.545636 105.4 77.508 109.060976 1856.411129 -540.682919
3 B Niger 2 768.4 179.594729 89.0 141.308 107.854786 575.540154 -93.584268 
WindowsPath('C:/Users/benny/OneDrive/Documents/Github/xdssat/docs/learn/data/module5/niger_farms.csv')

4. Things to try

  • Change WTHER of UFGA7812.SNX from W to M and use measured Gainesville weather files instead (dssat-csm-data has several years). Do the strategies keep their ranking?
  • Exercise 1 asks what happens when each irrigation costs $25 instead of $0.50. The page has a slider for it.
  • At Kadoma, plant a month later. Does the blanket N rate change?
  • Exercise 4: set up a seasonal experiment of your own, 4 to 8 treatments, at least 8 years, with prices that fit the place.
  • Do your own risk assessment: one crop, one decision, at least 20 seasons, and a statement of what you assumed.
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engine C:\TEMP\dsn\dssat\dscsm048.exe
csm_data_commit 99c95b340acb9515c2d0a8ab582f5fbbf076f345
csm_os_commit 25c93b9a2f73f8ec45bf441b198dac5fb7b22849
run_on 2026-11-06 23:53
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