the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 20 May 2026
Unified Conversion Equations between Olsen and Mehlich-3 Soil Phosphorus Tests
Abstract. Methods for soil test phosphorus (STP) differ globally and even within countries. While soil P tests often correlate, the relationship is often specific to a region or study, making any conversion equation difficult to transfer between contexts. Agronomic recommendations, P transport models, syntheses, and other works lack a strong basis for converting between STP. We fulfil this need for converting between two common STP measurements – Olsen P and Mehlich-3 P – through models which account explicitly for soil properties. Hypothesizing that soil properties at the sample level govern how STP values relate, we built models using a combined dataset of ca. 900 soils across the conterminous US and Canada, spanning 10 soil orders (USDA), 3 to 89 % clay, and pH 4 to 9. Model complexity ranged from conventional ‘region-level’ regressions (no soil data) to models adapting to many facets of soil P chemistry, presenting users several viable options suitable for their data context. Depending on data availability, the user could convert between Olsen P and Mehlich-3 P with half the error or less of conventional ‘region-level’ regressions. This reduction in conversion error impacts agronomic recommendations, environmental risk assessments (e.g., P index), and calibration of P transport models (e.g., SWAT+). While it remains best to simply measure the STP of interest, the conversion models here should prove useful in many contexts where that is not feasible. We provide the models in ready-to-use formats, depending on the covariates available to the user and whether the user wants to apply the equations in a spreadsheet or within model code.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-2518', Anonymous Referee #1, 19 Jul 2026
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RC2: 'Review of egusphere-2026-2518', Anonymous Referee #2, 20 Jul 2026
Simpson et al. present a rather technical but useful study on conversion equations between the two common soil P tests: Olsen P and Mehlich-3 P. The manuscript raises some interesting points and the conversion equations will surely be useful for future large-scale studies needing to harmonize soil P test data. However, in my opinion scientific depth (contextualization and discussion) and quality of writing should be improved in several places.
Major comments
I recommend to rename the datasets for this paper. The names legacy P and ALP are confusing, because legacy P is of course its own concept, but not really relevant for this paper. What about something simple like: pan_USA and case study datasets, or similar? Of course in the methods you can make the link to the projects.
Please start with a clear definition of labile P if that is going to be the word you use. Then be consistent in the wording.
Authors do not mention the broader limitations of STP in general: extracting P with an alkaline or acid solution is not process-based. Indeed for local agronomic applications yield response relationships are quantified. But an Olsen value of 15 mg/kg has a very different environmental / agronomic meaning in one soil than another. This is touched on a bit in the discussion but not enough and it should come already earlier as well. See also crop response e.g. (Hirte et al., 2021; Morel et al., 2021).
Why are sediments included? I don’t think M3 and Olsen P are used for sediments…
Fig 1: This figure could be improved. Why are ALP sites not plotted as points? What do the colors mean for the legacy P sites? Why not make color or point size as a function of sample size?
Data coverage: some areas are very sparely covered, while the legacy P sites are overrepresented with up to 100 samples per site. How did you account for this?
Please explain all the soil measurement methods in table 1, e.g. by including a reference for each method. What is EPC0? Is pH measured in water or KCl? How is total P measured? Clarity is important here if you want other people to be able to make use of your equations. Also it needs to be reproducible.
Authors should better explain the potential use of the harmonization between different soil P tests, either in the introduction and or the beginning of the discussion. Another important application is validation data for large global crop models or input data for digital soil mapping. Authors may consider also mentioning application for large scale/global soil property homogenization. See e.g. (McDowell et al., 2026, 2023), where soil test data from many different STPs was used.
Authors need to discuss: the “unified” conversion equations are calibrated on USA and Canada soils. What is the usefulness for the rest of the world?
The discussion of the underling mechanisms (section 4.2) needs major revision to reach a deeper level of understanding P dynamics. Writing, structure, and depth need to be improved. The discussed mechanisms make sense for the acidic test M3, but not at all for Olsen P which has a pH of 8.5. The fact that both of these tests are assumed to extract “plant available P” already becomes interesting by just comparing the pH values of the extractants. Sure the difference in time scale is there, but the pH difference is more important since we’re extracting through completely different mechanisms.
Interesting discussion on implications for fertilizer recommendations (section 4.3) with tangible examples.
Section 4.4. could start a bit broader, since hydrological modeling is an important but not the only environmental use of STPs.
Minor comments
l. 42 authors may consider broadening here to include another recent use of STP: input for large-scale modelling applications
l. 74-76 This is a non-exhaustive listing of places where these tests are used. To make the manuscript more interesting for a global readership, please list also other world regions where the tests are used, not only the anglo-saxon countries.
l. 83 “P lability chemistry”? This seems like strange wording. Perhaps: soil properties governing P exchange kinetics? This is a valid and important hypothesis, but comes a bit out of no-where. I think a few more sentences on P chemistry and exchangeability are warranted in the introduction, linking to latest state of the art understanding of P species and their turnover.
l. 93 Not clear what ~90 per site refers to.
l. 139 in R? or python?
l. 149 is “awkward” the right word? Seems pretty colloquial
Fig. 2 “dataset” is cutoff on the right side
l. 250 “ may speak to” please use precise language
l. 307-308 “in comparison to region-level regressions” this is one specific application. But I think in global studies they even use one global equation. Please check and discuss also there the impact. The good news here is really that these basic soil properties that lead to such drastic improvements in prediction are usually readily available
l. 339 section title should be improved
l. 356 This sentence needs to be rewritten. No need to accuse Olsen and Mehlich of shortsightedness post-mortem ;)
l. 356 what is means with P lability dynamics? Please use precise language and aligned with state-of-the-art understanding of P cycling in soils.
l. 362 I think here the word lability is used not for P exchangeability but for statistics? Please choose another word to avoid confusion
l. 366-367 Delete or improve this sentence
l. 391 “were predictive”?
l. 391 “power” is not the right word. Please use precise scientific language.
4.3 might want to mention large-scale / global P limitation modelling in crop models. For that you also often need to harmonize soil P test data from different tests.
l. 472 “ germane”?
l. 472-475. Why conditional tense? People are already working on this.
l. 539 change “the success we found here” to precise language
l. 545 I recommend to avoid abbreviations or re-introduce them in the conclusion. Some readers will only look at the conclusion.References
Note: references are to support my argumentation only. Not a recommendation of papers to cite.
Hirte, J., Richner, W., Orth, B., Liebisch, F., Flisch, R., 2021. Yield response to soil test phosphorus in Switzerland: Pedoclimatic drivers of critical concentrations for optimal crop yields using multilevel modelling. Sci. Total Environ. 755, 143453. https://doi.org/10.1016/j.scitotenv.2020.143453
McDowell, R.W., Noble, A., Pletnyakov, P., Haygarth, P.M., 2023. A Global Database of Soil Plant Available Phosphorus. Sci. Data 10, 125. https://doi.org/10.1038/s41597-023-02022-4
McDowell, R.W., Noble, A.D.L., Doscher, C., Helfenstein, J., 2026. An improved global database and model of plant available soil phosphorus. Sci. Data 13, 880. https://doi.org/10.1038/s41597-026-07140-3
Morel, C., Plénet, D., Mollier, A., 2021. Calibration of maize phosphorus status by plant-available soil P assessed by common and process-based approaches. Is it soil-specific or not? Eur. J. Agron. 122, 126174. https://doi.org/10.1016/j.eja.2020.126174Citation: https://doi.org/10.5194/egusphere-2026-2518-RC2
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- 1
The authors propose in this manuscript a statistical approach allowing to convert Olsen P data (OlsP) into Mehlich 3 P (M3P) data and reciprocally, taking into account important soil properties at sample level. This is by itself a good idea as more and more scientists working on reviews and on models need such conversion functions to transform often heterogeneous databases on soil available P in a single usable indicator. Using data collected in two databases (Legacy P project and ALP) from North America the authors show that the ratio OlsP to M3P strongly differ among sites, so the use of a single ratio would lead to wrong conversions. They also show that this ratio can be successfully predicted when integrating appropriate soil properties into their models, the best being the GLM M3P model. This manuscript is interesting but still needs to undergo major revisions before it can be accepted.
Major comments:
This paper implicitly makes the hypothesis that each soil will have a single OlsP or M3P value that will be independent from the laboratory where it will be analyzed. However, that might not be always the case. A study by Lischer and Neyroud (2003, journal of plant nutrition and soil science 166, 422-431) showed that OlsP measured on same 135 soils sent to various European laboratories could in average vary by a factor of 2. The conclusion of this paper was that if the protocols are not detailed enough and/or not strictly followed, then the risk that different labs using theoretically the same protocol would obtain different results would be important. Was this risk considered in this paper submitted to SOIL? How many laboratories were involved in total? Was at least a representative subset of samples sent to each of these labs and were the results compared? If this has been done for the data used in this paper, this needs to be said (the reviewer did not look at the Simpson et al 2025 paper mentioned at line 103). If it has not been done, the uncertainties linked to the laboratories need to be addressed explicitly in the discussion. The other soil analysis methods, their justification for this specific work, and the references where the protocols can be found should also be mentioned for the sake of transparency.
The authors mention often the concept of intensity, capacity and quantity. I reckon that it is an old albeit useful concept, but if this is important to the authors, these terms should be clearly defined and related to the soil P parameters considered here. Furthermore, the authors use very often the terms labile and lability. These terms are often used in literature but unfortunately with unclear and variable meanings. I suggest that these terms are removed from the text and replaced by well defined terms.
The discussion is too long (from line 300 to line 543 on a paper that has in total 562 lines). I suggest that the authors strongly decrease it. For instance, section 4.2 which attempts to use the results of the statistical analyses presented in this paper for a mechanistic discussion on soil inorganic P availability is really too long and do not bring any new information compared eg to the works of Barrow, Fardeau, Morel, van der Zee...
Specific comments
Line 83, what is P lability chemistry?
Line 213, Le Suer is to be corrected to Le Sueur.
Line 304, what is a fertility recommendation?
Line 356, what is P lability dynamics?
Line 408, what is a crop correlation?