Modeling integrated soil fertility management for maize production in Kenya using a Bayesian calibration of the DayCent model

Laub, Moritz; Necpalova, Magdalena; Van de Broek, Marijn; Corbeels, Marc; Ndungu, Samuel Mathu; Mucheru-Muna, Monicah Wanjiku; Mugendi, Daniel; Yegon, Rebecca; Waswa, Wycliffe; Vanlauwe, Bernard; Six, Johan

doi:https://doi.org/10.5194/bg-21-3691-2024

Articles | Volume 21, issue 16

https://doi.org/10.5194/bg-21-3691-2024

© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/bg-21-3691-2024

© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 21, issue 16

Research article

|

22 Aug 2024

Research article |

| 22 Aug 2024

Modeling integrated soil fertility management for maize production in Kenya using a Bayesian calibration of the DayCent model

Moritz Laub, Magdalena Necpalova, Marijn Van de Broek, Marc Corbeels, Samuel Mathu Ndungu, Monicah Wanjiku Mucheru-Muna, Daniel Mugendi, Rebecca Yegon, Wycliffe Waswa, Bernard Vanlauwe, and Johan Six

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Final revised paper (published on 22 Aug 2024)
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Preprint (discussion started on 21 Aug 2023)

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-1738', Anonymous Referee #1, 26 Sep 2023

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1738/egusphere-2023-1738-RC1-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2023-1738-RC1
- AC1: 'Reply on RC1', Moritz Laub, 12 Dec 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1738/egusphere-2023-1738-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-1738-AC1
CC1:
'Comment on egusphere-2023-1738', David Pelster, 29 Sep 2023

General comments: Very nice paper. Generally well written. The M&M in particular are very thorough. I have not done much modeling, but I found that the M&M did a good job of explaining the model parameters and their calibration along with how sensitive they were. Apart from a bunch of small issues (see below), I found that the discussion around objective iii. was lacking a bit. What I was really looking forward to was more discussion around the trade-offs between yield and SOM / increases along with the global warming potential of the different ISFM treatments.
Specific comments:
Lines 85-90: A map with the site locations would be helpful here as well.
Line 118 : should be “CH4 oxidation”.
Lines 150-155: How many samples per chamber? How long was the deployment time? How did you calculate the change in mixing ratios over time (linear or non-linear?), how were gas samples analyzed? (on a GC? What kind?). You need a bit more detail here.
Line 367: Is “langley” an SI unit? I had to do an internet search to find out what it is. Would it be possible to explain what this is? Or convert to SI units?
Figure 2: shouldn’t there be some label on the X and Y axes?
Line 395: perhaps I don’t quite understand, but isn’t the systemic underestimation at high yields (and AGB) a “bias”?
Line 446: wouldn’t a negative reduction be an increase?
Line 447: I would say “led to” rather than “could lead to”. Since there was a reduction noted.
Figure 7: It seems that you are unable to simulate the high emission days, which could be why the cumulative simulated emissions are typically lower than the 1:1 line. Also, in the Sidada site for simulate vs measured cumulative emissions, you have one data point that has a lot of leverage. I would consider seeing how the regression line looks without that point. And maybe investigate why that point is so different from the rest of the data at that site.
Lines 483-484: Mention here that DayCent overestimated SOC pre-calibration, but after the calibration the SOC concentrations (or stocks) were simulated much more accurately. This difference is clear when you look at the figure, but since the figure is in the appendix, it may not be readily apparent to the readers.
Line 513: why do you use 2¹ and 2³ here? Why not just say 2 and 8? Or am I missing something?
Lines 526 to 529: Is there a reason why you switch between SOC and SOM? It seems like you are talking about the same thing.
Line 534: “vary” not “very”.
Line 543: Are you saying that DayCent does not capture yield increases above 100-150 kg N per ha per season in general? Or just specifically in Kenya. I have not used DayCent, but I would be very surprised if it does not capture yield increases above 150 kg N per ha in temperate regions.
Line 549-553: I wouldn’t worry too much about the poor match between simulated and measured daily fluxes. I would mention though that the timing of peak fluxes is related more to soil gas diffusivity and that soil hydraulics are more just a proxy of the diffusivity.
Line 553: Sommer et al. 2016 does not quite say this. What they say is that “As such, the overall model fit was exceptionally good, even though the visual impression would suggest a significant overestimation of emissions by CropSyst”. If you look at the figures in their study, the simulated line up very well with the measured emissions. It is just that there are a lot of peaks in the simulated that occur between samplings.

Line 569: I guess this is somewhat true, in that maize mono-cropping will still produce some GHG emissions. However what is the difference between the ISFM practices and the “typical” treatment (what is typical? No inputs? No N input and a small amount of FYM)? It seems like adding some inorganic N with 1.2 T C increased yields, without increasing yield scaled emissions compared with 0N 0C and compared with 0n 1.2T C. So even though it is not exactly “negative emission technology” it still seems to be an improvement.
Line 570: why say “positive absolute” in stead of just “positive”?
Lines 578-580: While I agree that N fertilizer should only be applied to responsive soils, I’m not sure that is a conclusion of the date that you have here. If you look at yields, all the sites respond to N fertilizer (either mineral or organic). It is just that they seem to respond a bit differently, particularly in the N2O emissions, to the fertilizer applications. Besides, the 0N control also has much higher yield scaled GWP in Embu and Machanga, mainly related to loss of SOC, so I don’t think the higher yield scaled emissions (compared with Sidada and Aludeka) with the +N treatments indicate that these shouldn’t be fertilized. In fact, the decrease in yield-scaled GWP when adding N is greater at the sites in Central Kenya than they are at Sidada, which almost contradicts what you are saying here.
Line 610: Just mention which treatment had the lowest yield-scaled emissions (the mix of FYM +N) as the preferred INMS for Kenya.
Table A1: can you add the sand content as well?
Figure A3: what depth are you using to calculate the stocks? You mention 15 cm depth in some locations, but you also mention that DayCent uses 20 cm depth. And, I am having a hard time seeing how the Machanga site lost so much of its C. at 20 cm depth a soil with a C content of 0.3 and a BD of 1.51 would have about 10 t C per ha. And you are saying here that it lost about 10 t per ha (or essentially all of its soil C). Is my math off (wouldn’t be the first time).
Figure A6: the figure caption needs to be re-done. For example, the second sentence is missing a word somewhere (perhaps “was” before “insensitive”?). And secondly, are you sure about the 50/50 split application? You were calibrating to data where the split application was 40 kg N at planting and 80 kg after ~ 6 weeks (see line 107-108; also line 165).
Figure A10, can you increase the font size in the figure please?

Citation: https://doi.org/10.5194/egusphere-2023-1738-CC1
- AC3: 'Reply on CC1', Moritz Laub, 12 Dec 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1738/egusphere-2023-1738-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-1738-AC3
RC2:
'Comment on egusphere-2023-1738', Anonymous Referee #2, 06 Nov 2023
The paper, entitled “A robust DayCent model calibration to assess the potential impact of integrated soil fertility management on maize yields, soil carbon stocks and greenhouse gas emissions in Kenya” emphasizes the importance of model calibration to enhance model accuracy. It utilizes a rich dataset from 4 sites in Kenya, an area that has been less represented/explored by many process-based models like DayCent, and thus, it provides a substantial amount valuable information. Furthermore, the paper centers its focuses on integrated soil fertility management (ISFM), maize yield, soil organic carbon, and greenhouse gas emission. Nevertheless, there are numerous concerns regarding the model calibration process (see Specific Comments section) and recommend a major revision to address these concerns before considering it for publication.
General Comments:
Line 106: it was not clear whether organic resources were applied once per year or once per season. Provide clarification.

Section 2.3.3: Provide more detailed information on historical cropping and specify the simulation periods for reproducibility, preferably in a table format. Additionally, include information of the optimal duration of cropping systems following the transition from native condition to achieve the initial SOC levels. It would be helpful to provide a figure showing the time series of SOC stocks for the entire simulation including native condition and historic cropping systems for each site.

In Section 2.5, provide the equation for the likelihood function used in the Bayesian calibration. Additionally, clarify whether the same likelihood function was employed for the GSA, and mention this in the text.

Line 292-293, provide reference(s) for the statement, “Due to the large number of observations and the mostly balanced dataset, the off-diagonal elements were set to 0”. Considering the higher autocorrelation in the time series for the modeled SOC stock, the statement may not hold true.

In Figure 7, the caption mentioned “variance (measurements)”. It is unclear whether the error bars represent variance, standard deviation, or 95% confidence interval. If variance is presented as error bars, this is unusual. Replace “variance” with “95% confidence interval” to main consistency consistent.

Figure 8 shows the difference relative to CT-N. It would be informative to show the relative differences in comparison to business-as-usual practices, as this would help identify and recommend management changes for better management practices.

In Table A1, include not only clay (%) but also sand (%) and silt (%) as required by DayCent for reproducibility.

In Figure A2, it is evident that measured SOC stock has been declining since the starting year. It would be helpful to discuss potential reasons for the decline and why model simulation is able to predict the decline.

Specific Comments:
The manuscript employs a two-step process for model predictions: Step 1 involves running the model with one set of model parameters (i.e., native condition and historical simulation) up to the beginning of experiment (i.e., initial measurement of SOC). This is done with limited adjustment to better align the model’s output with measured SOC. In Step 2, a model calibration is performed, updating various parameters to a different value, with some exhibiting significant changes of several magnitude, especially the decomposition rate of slow and passive pools. Extending the model simulation with the change in parameters may disrupt the equilibrium condition and induce a drift effect, where the model attempts to reach a new equilibrium condition due to parameter changes. This makes it challenging to determine whether the changes in SOC stocks are due to alteration in management practices or change in model parameters. The potential impacts of this should be thoroughly investigated. Additionally, in line 610, the authors claims that the newly calibrated model is applicable for “upscaling the model to larger areas in Kenya” without providing practical recommendations for simulations when two sets of model parameters are available. The associated risks of such recommendations should also be examined. To mitigate potential risk, I would recommend using a model calibration procedure that results in a single set of model parameters or joint posterior distribution.

The manuscript utilizes initial parameter value for SOM decomposition, as reported in Gurung et al. (2020), which were suitable for SOC in the top 30 cm. However, the modeled SOC stocks were compared against measured SOC stocks up to a depth of 20 cm, thus resulting in a non-equivalent comparison. This inconsistency is evident in Figure A7, where the reported model predictions consistently show higher values than the measured SOC.

IPCC recommends modeling SOC to a depth of 30 cm for GHG accounting and reporting. Since SOC measurements to 30 cm were available, it would be more appropriate to calibrate the model to simulate SOC to 30 cm, aligning it with the IPCC’s recommendation.

The manuscript employs a “leave-one-site-out” cross-validation approach; however, the analysis and results of the cross-validation were not presented. I recommend including some detail about the cross-validation process and its results in the manuscripts.

Technical Corrections:
Line 324: move the explanation “O___{_y the mean of the y-th type of measurement” below equation-9.}

Line 335: mass unit for CO2eq/ha/yea) is missing.

In the caption for Figure 7, replace “95% confidence intervals” with “95% credible intervals” for BC.
Citation: https://doi.org/10.5194/egusphere-2023-1738-RC2
- AC2: 'Reply on RC2', Moritz Laub, 12 Dec 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1738/egusphere-2023-1738-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-1738-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Reconsider after major revisions (30 Dec 2023) by Lutz Merbold

AR by Moritz Laub on behalf of the Authors (04 Apr 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (24 Apr 2024) by Lutz Merbold

RR by Anonymous Referee #3 (02 May 2024)

RR by Anonymous Referee #1 (03 May 2024)

RR by Anonymous Referee #2 (16 May 2024)

Suggestions for revision or reasons for rejection

The revision has addressed many of the issues raised in the first review. There has been a significant improvement in the content, flow, and structure, which has increased the readability of the manuscript. In addition, authors have incorporated two significant changes in the methodology section: (1) the selection of prior, and (2) the initialization of SOC pools. Reviews of this newly added section are provided in the subsequent paragraphs. Another area of concern is in the newly updated result section 3.2, which reported the posterior estimates from the inverse modeling using SIR algorithms. Here, the marginal distribution for the posterior is similar to the marginal distribution from the prior, indicating little or no influence of the dataset on the posterior suggesting nothing is learned from the data assimilation exercise. This is contrary to the title’s claim of “robust DayCent model calibration …”. For these reasons, I recommend a major revision before recommendation for publication. More details are provided below:

SOC pool initialization: One of the major changes involved replacing the long historical simulation with measured SOC, which was adjusted backward in time and initialized at the start of the Experiment. With the update, the posterior parameter can be defined as p(θ|D,M,MAOM) and now conditions on data (D), model (M) and measured mineral associated organic matter (MAOM). Therefore, any future simulation leveraging this study and aiming to understanding the regional or national GHG balance within SSA, as represented by the four-experiment station, now also requires measured or estimated value of MAOM. Therefore, the simulation approach, which requires MAOM measurement, may limit broader use of the model in SSA region. Furthermore, the initialization of SOC pools in the process-based ecosystem model may introduce significant bias in the model’s estimates of SOC stock changes (Fallon and Smith, 2000, Zhou et. al., 2023). Both methods: (1) long historical simulations to equilibrium and (2) initializing model pools with measurement—have been extensively studied and used in literature. In my personal viewpoint, both methods are equally valid given adequate testing and reasoning. Both methods have strengths and weaknesses. The strength led to higher accuracy, while the weaknesses can introduce significant bias and contributing toward higher uncertainty.

Prior distribution: Another significant change in the updated manuscript is the introducing of a new prior distribution during the SIR step. As a result, the revised manuscript uses two sets of prior distribution: a uniform prior for the global sensitivity analysis, and a Gaussian prior for the SIR step. This is uncommon and generally not accepted in Bayesian inferences, as the prior is considered our initial beliefs about an uncertain parameter before observing any data. Therefore, introducing two beliefs for the same set of parameters in the model is unusual. The authors selected coefficients of variations ranging between 5% and 30% for DayCent parameters based on the level of range provided in its manual. However, they did not provide details on how these selection for coefficient of variation satisfy one of the requirements for SIR or similar method, which is that the prior range should cover the entire range of the posterior (Galman, 2014). Also, more detail should be provided on the choice for the coefficient of variation to convincing demonstrate that the empirical data suggest that the prior range is adequate enough for the theoretical understanding of these parameters.

Posterior distribution: The manuscript calibrated 13 model parameters after conducting a parameter screening using the GSA. In section 3.2 of the results, the posterior was presented in Figure 2. Throughout the text, a single parameter estimate was provided, but it was not specified which statistics (e.g., mean, mode, median, etc.) was presented. The posterior should be summarized with sufficient statistics, such as the mean, standard deviation, and 95% credible intervals. If the single parameter estimates the mean, mode, or median, there is a significant disagreement between the text and the figure for parameters clteff(1,2,&4) and pmco2(1&2). The reported posterior estimates of 19.1 and 0.82 fall well outside the curve region with higher density. I believe this could be a miscalculation or misinterpretation, and should be thoroughly investigated.

Some minor comments and corrections:

Line 20-23: The author claim that: “The model performance and the match between the cross-evaluation posterior credibility intervals for different sites indicated the robustness of the model parameterization and the reliability of the DayCent model for spatial upscaling of simulation.” However, the manuscript did not perform a large-scale simulation, and the claim for “spatial upscaling” should be removed or justified.

Line 23: provide quantitative values (i.e., EF for daily N2O) instead of just mentioning negative value.

Line 70: The terms “validated” and “evaluated” were used interchangeably throughout the manuscript. For instance, in line 9, “cross-evaluation” is used but in line 164, “cross-validation” is used.

Line 102: If the mitigation of CO2 emissions is due to C sequestration, it would be advisable to use the term “C sequestration” instead of “mineralization of SOC”

Line 134: Should this
“Tithonia diversifolia (TD) green manure and Calliandra calothyrsus (CC) prunings, low quality stover of Zea mays (MS) and sawdust from Grevillea robusta trees (SD), locally available farmyard manure (FYM) and a control treatment”

be written as following.

“Tithonia diversifolia (TD) green manure, Calliandra calothyrsus (CC) prunings, low quality stover of Zea mays (MS), sawdust from Grevillea robusta trees (SD), locally available farmyard manure (FYM) and a control treatment”

In Table 1. values for model parameters and coefficient of variation seems truncated given the table description (i.e., parameter values and coefficient of variations were missing)

Equation before line 185, if SOC stock estimates are for 0-30 cm as IPCC-recommended, it should be:

〖SOC〗_30 (kg 〖ha〗^(-1) )= (1- β^30)/(1-β^15 )*〖SOC〗_15

Provide the value used for beta^15 and beta^30 used in the equation. The equation number is also missing.

Line-261, it is a little confusing and not clear what the author wants to convey. Specifically, data availability and which model parameters and value used for initialization.

Line-266: It was not clear whether the author’s discussion about aboveground biomass (AGB), yield (Y), and harvest index (HI) is based on the measured data or modeled values. In DayCent Y = HI*AGB (for grain crops). However, the parameter HIMAX (maximum harvest index) is adjusted due to stress to (HI <= HIMAX).

Line-395: Please clarify what multiply/divided by 3 and 10 means. Maybe it is self-explanatory when full view of Table-1 is available.

Equaton-3: The Likelihood function provided in Equation-3 is applicable to only one type of measurement, such as Yield or SOC. Please provide details on how multiple likelihoods—for SOC, Yield, and Harvest Index were combined, if at all, for the final Bayesian calibration. If they were not combined, please provide an explanation.

Line 571: The posterior credibility intervals in analog to confidence intervals in frequentist statistics and posterior prediction interval analog to prediction intervals. The coverage probability (i.e., 95% of observed) within the 95% Posterior prediction interval is only valid comparison but not with posterior credibility intervals (note that posterior credibility interval < posterior prediction interval).

Prove all the missing equations used in the analysis, (one such example is the equation for aggregated model output for the GSA) in the supplementary section.

Reference:
Falloon, P. D., & Smith, P. (2000). Modelling refractory soil organic matter. Biology and Fertility of Soils, 30(5–6), 388–398. https://doi.org/10.1007/s003740050019

Zhou, W., Guan, K., Peng, B., Margenot, A., Lee, D., Tang, J., Jin, Z., Grant, R., DeLucia, E., Qin, Z., Wander, M. M., & Wang, S. (2023). How does uncertainty of soil organic carbon stock affect the calculation of carbon budgets and soil carbon credits for croplands in the U.S. Midwest? Geoderma, 429, 116254. https://doi.org/10.1016/j.geoderma.2022.116254

Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B., 2014.Bayesiandata analysis, Third edit. ed, BDA3. Boca Raton : CRC Press, Boca Raton.

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ED: Publish subject to minor revisions (review by editor) (26 May 2024) by Lutz Merbold

Dear Moritz Laub,

you revised version of the manuscript: "A robust DayCent model calibration to assess the potential impact of integrated soil fertility management on maize yields, soil carbon stocks and greenhouse gas emissions in Kenya" has undergone a second round of reviews (3 reviewers). All reviewers are in agreement that the manuscript has improved considerable, with two suggesting some minor revisions including some clarifying questions and adjustments (revs 2 and 3) whereas the 3rd reviewer remains still critical (see the comments from rev 1 this text). This is particularly the case for the prior and posterior distribution which need to be addressed. This should be achievable relatively straight forward. Similarly the individual minor suggestions for the manuscript provided by all three reviewers can be incorporated right away. Following this, I am accepting the manuscript for publication in BG with subject to minor revisions.

with kind regards

Lutz Merbold

Prior distribution: Another significant change in the updated manuscript is the introducing of a new prior distribution during the SIR step. As a result, the revised manuscript uses two sets of prior distribution: a uniform prior for the global sensitivity analysis, and a Gaussian prior for the SIR step. This is uncommon and generally not accepted in Bayesian inferences, as the prior is considered our initial beliefs about an uncertain parameter before observing any data. Therefore, introducing two beliefs for the same set of parameters in the model is unusual. The authors selected coefficients of variations ranging between 5% and 30% for DayCent parameters based on the level of range provided in its manual. However, they did not provide details on how these selection for coefficient of variation satisfy one of the requirements for SIR or similar method, which is that the prior range should cover the entire range of the posterior (Galman, 2014). Also, more detail should be provided on the choice for the coefficient of variation to convincing demonstrate that the empirical data suggest that the prior range is adequate enough for the theoretical understanding of these parameters.

Posterior distribution: The manuscript calibrated 13 model parameters after conducting a parameter screening using the GSA. In section 3.2 of the results, the posterior was presented in Figure 2. Throughout the text, a single parameter estimate was provided, but it was not specified which statistics (e.g., mean, mode, median, etc.) was presented. The posterior should be summarized with sufficient statistics, such as the mean, standard deviation, and 95% credible intervals. If the single parameter estimates the mean, mode, or median, there is a significant disagreement between the text and the figure for parameters clteff(1,2,&4) and pmco2(1&2). The reported posterior estimates of 19.1 and 0.82 fall well outside the curve region with higher density. I believe this could be a miscalculation or misinterpretation, and should be thoroughly investigated.

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AR by Moritz Laub on behalf of the Authors (13 Jun 2024) Author's response Author's tracked changes Manuscript

ED: Publish as is (04 Jul 2024) by Lutz Merbold

AR by Moritz Laub on behalf of the Authors (05 Jul 2024)

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Short summary

We used the DayCent model to assess the potential impact of integrated soil fertility management (ISFM) on maize production, soil fertility, and greenhouse gas emission in Kenya. After adjustments, DayCent represented measured mean yields and soil carbon stock changes well and N₂O emissions acceptably. Our results showed that soil fertility losses could be reduced but not completely eliminated with ISFM and that, while N₂O emissions increased with ISFM, emissions per kilogram yield decreased.