{"id":7419,"date":"2026-06-16T09:14:43","date_gmt":"2026-06-16T15:14:43","guid":{"rendered":"https:\/\/astfilters.com\/aquatic-systems\/?post_type=edu_article&p=7419"},"modified":"2026-06-16T09:17:49","modified_gmt":"2026-06-16T15:17:49","slug":"linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras","status":"publish","type":"edu_article","link":"https:\/\/astfilters.com\/aquatic-systems\/articles\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras","title":{"rendered":"Linear vs. Monod Modeling for Ammonia Oxidation in Low-TAN RAS"},"content":{"rendered":"

[et_pb_section fb_built=”1″ _builder_version=”4.27.6″ _module_preset=”default” custom_margin=”|0px||0px|false|false” custom_padding=”0px|0px|0px|0px|false|false” global_colors_info=”{}”][et_pb_row _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_text _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n

In low-TAN marine hatchery, broodstock, and fingerling systems, peak biofilter capacity is not always the most important design question. A simple linear model, calibrated only in the low-ammonia range, can be a more stable and practical way to estimate ammonia oxidation.<\/h2>\n

Estimated read time: 8 minutes | Audience: aquaculture students, educators, RAS designers, hatchery teams, and water-quality professionals<\/em><\/p>\n

Educational summary adapted from Malone, Bergeron, and Cristina (2006), Linear versus Monod representation of ammonia oxidation rates in oligotrophic recirculating aquaculture systems.<\/em><\/p>\n

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Key takeaways<\/h2>\n
    \n
  • Low-TAN systems need a different design focus.<\/strong> Marine broodstock, larval, and fingerling systems often operate at very low total ammonia nitrogen (TAN), so low-range accuracy matters more than peak carrying capacity.<\/li>\n
  • A broadly calibrated Monod model can mislead low-TAN design.<\/strong> Monod kinetics are useful, but a single curve calibrated across high and low loading conditions may not accurately represent the oligotrophic range.<\/li>\n
  • Organic loading can suppress nitrification.<\/strong> As organic loading rises, fast-growing heterotrophic bacteria can interfere with nitrifiers and cause ammonia oxidation capacity to decline – a behavior the standard Monod curve does not represent.<\/li>\n
  • The paper supports a zero-intercept linear model for the low-TAN range.<\/strong> For TAN values around 0.1 to 0.5 g-TAN\/m3<\/sup>, the authors found that VTR = \u03c4A<\/code> gave more stable parameter estimates than the traditional Monod approach.<\/li>\n
  • The slope, \u03c4, can become a practical biofilter rating.<\/strong> A higher \u03c4 value means greater TAN conversion per unit biofilter volume at a given low TAN concentration, as long as comparisons are made under similar conditions.<\/li>\n<\/ul>\n

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    Why low-TAN biofilter modeling matters<\/h2>\n

    Recirculating aquaculture systems (RAS) rely on biofilters to convert ammonia produced by fish, shrimp, or other aquatic organisms. In many growout systems, operators may focus on maximum ammonia removal capacity. In marine hatcheries and broodstock systems, the design problem is different: the system must maintain consistently low ammonia concentrations for sensitive animals and early life stages.<\/p>\n

    The paper identifies common TAN targets for these applications:<\/p>\n\n\n\n\n\t\n\n\t\n\t\n\t
    Application<\/th>Typical TAN target discussed in the paper<\/th>Why it matters<\/th>\n<\/tr>\n<\/thead>\n
    Marine broodstock<\/td>0.1-0.3 g-N\/m3<\/td>Supports long-term conditioning and reproductive performance.<\/td>\n<\/tr>\n
    Larval systems<\/td>Less than 0.1 g-N\/m3<\/td>Protects especially sensitive early life stages.<\/td>\n<\/tr>\n
    Fingerlings<\/td>Less than 0.5 g-N\/m3<\/td>Maintains water quality during nursery production.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n
    \n

    Unit note:<\/strong> In water, g\/m3<\/sup> is numerically equivalent to mg\/L. A TAN target of 0.5 g\/m3<\/sup> is the same as 0.5 mg\/L.<\/p>\n<\/section>\n

    \n

    What VTR means<\/h2>\n

    The paper focuses on volumetric TAN conversion rate<\/strong>, or VTR<\/strong>. VTR describes how much total ammonia nitrogen a biofilter converts per unit biofilter volume per day.<\/p>\n<\/section>\n

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    Plain-language definition<\/h3>\n

    VTR asks: How much ammonia can this biofilter remove at the TAN concentration the system is actually allowed to reach?<\/strong><\/p>\n

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    A biofilter may show impressive conversion rates under high ammonia conditions, but a hatchery system may never be allowed to approach those concentrations. For low-TAN systems, the most relevant performance question is how the filter behaves near the target operating range.<\/section>\n
    \n

    <\/h2>\n

    The traditional Monod approach<\/h2>\n

    Biofilter nitrification is often modeled with a Monod-style relationship:<\/p>\n<\/section>\n

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    Monod \/ hyperbolic model<\/h3>\n

    VTR = (VTRmax<\/sub> x A) \/ (kb<\/sub> + A)<\/span><\/p>\n

    Where VTRmax<\/code> is the maximum modeled conversion rate, A<\/code> is TAN concentration, and kb<\/code> is the apparent half-saturation constant.[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_text _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n

    This model creates a hyperbolic curve: VTR rises quickly at low TAN, then approaches a maximum as TAN increases. That shape can be useful, but the paper highlights two problems for low-TAN RAS design.<\/p>\n

    First, traditional calibration methods often use data across a broad TAN range, including higher TAN concentrations that are not representative of hatchery or broodstock operation. That can bias the curve away from the range where low-TAN systems actually operate.<\/p>\n

    Second, a standard Monod curve does not show the collapse in nitrification capacity that can occur under high organic loading. The model approaches a maximum; real biofilters can lose performance when organic matter promotes heterotrophic growth that interferes with nitrifiers.<\/p>\n

     <\/p>\n<\/section>\n

    \n

    Why organic loading changes the picture<\/h2>\n

    Nitrifying bacteria are not alone in a biofilter. Heterotrophic bacteria grow on organic matter from feed, feces, and dissolved wastes. Under low biochemical oxygen demand (BOD), biofilms can remain relatively thin and dominated by nitrifiers. Under high BOD, faster-growing heterotrophs can form thicker layers that limit ammonia diffusion to the nitrifying bacteria below.<\/p>\n

    The paper describes this as heterotrophic interference<\/strong>. In practical terms, adding more loading does not always mean the biofilter keeps converting more ammonia. At sufficiently high organic loading, TAN conversion can decline.<\/p>\n

    The low-TAN linear model<\/h2>\n

    For the oligotrophic and mesotrophic range, the authors propose a simpler relationship:<\/p>\n<\/section>\n

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    Direct linear model<\/h3>\n

    VTR = \u03c4A<\/span><\/p>\n

    Where A<\/code> is TAN concentration and \u03c4<\/code> is the slope of the relationship between TAN and VTR. The intercept is forced to zero, meaning VTR is zero when TAN is zero.[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_text _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n

    This does not claim that all biofilter behavior is linear under all conditions. It is a targeted design simplification for low TAN concentrations, especially around 0.1 to 0.5 g-TAN\/m3<\/sup>.<\/p>\n

    The benefit is practical: instead of estimating two Monod parameters that may be unstable, the designer estimates one low-range slope. The authors call this slope a normalized conversion capacity.<\/p>\n<\/section>\n

    \n

    <\/h2>\n

    How the study compared the models<\/h2>\n

    The authors used two lines of evidence. First, they generated simulated biofilter data using a Monte Carlo approach under an assumed inhibition pattern. This let them test how different calibration methods behaved when the underlying process included nitrification inhibition at higher loadings.<\/p>\n

    Second, they compared the same modeling approaches using two field data sets from bead filter studies. The paper evaluated how well each method predicted VTR only within the low-TAN range.<\/p>\n\n\n\n\n\t\n\n\t\n\t
    Model approach<\/th>Calibration range<\/th>Main idea<\/th>\n<\/tr>\n<\/thead>\n
    Monod \/ hyperbolic model<\/td>Broad available range, up to about 5.0 g-TAN\/m3 in the Monte Carlo analysis<\/td>Fit one curve across both low and higher loading conditions.<\/td>\n<\/tr>\n
    Direct linear regression<\/td>Local low-TAN range, about 0.1-0.5 g-TAN\/m3<\/td>Fit the range that matters most for oligotrophic and mesotrophic operation.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n

    What the study found<\/h2>\n

    Across the Monte Carlo analysis, the linear model produced more stable parameter estimates. The coefficient of variation for \u03c4<\/code> was reported at about 7-8%. By comparison, the reported coefficient of variation ranged from 22-143% for VTRmax<\/code> and 29-137% for the apparent half-saturation constant in the Monod model.<\/p>\n<\/section>\n

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    7-8%<\/strong><\/h3>\n

    Coefficient of variation reported for \u03c4<\/p>\n

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    22-143%<\/strong><\/h3>\n

    Coefficient of variation reported for VTRmax<\/sub><\/p>\n

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    29-137%<\/strong><\/h3>\n

    Coefficient of variation reported for the Monod half-saturation constant<\/p>\n

    [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_text _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”]The linear model also produced a lower sum of squared errors than the Monod model for the low-TAN range in all four Monte Carlo parameter combinations tested. The paper reports this difference as statistically significant.<\/p>\n

    Field data showed the same directional pattern. In the Chitta data set, the low-range SSE was 474,303 for the direct linear regression and 508,660 for Monod kinetics. In the Pfeiffer and Malone data set, the low-range SSE was 3,981 for direct linear regression and 4,280 for Monod kinetics.<\/p>\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t
    Finding<\/th>Plain-language meaning<\/th>\n<\/tr>\n<\/thead>\n
    \u03c4 coefficient of variation: 7-8%<\/td>The single linear slope was comparatively stable across simulated data sets.<\/td>\n<\/tr>\n
    VTRmax coefficient of variation: 22-143%<\/td>The Monod maximum-rate estimate varied much more.<\/td>\n<\/tr>\n
    kb coefficient of variation: 29-137%<\/td>The Monod half-saturation estimate also varied substantially.<\/td>\n<\/tr>\n
    Direct linear regression had lower low-range SSE in the Monte Carlo analysis<\/td>The low-TAN linear fit better matched the range of interest in the simulations.<\/td>\n<\/tr>\n
    Direct linear regression also had lower low-range SSE in two field data sets<\/td>The field comparisons supported the same practical direction, though the authors called for more data.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n

    How \u03c4 can be used as a biofilter rating<\/h2>\n

    The paper suggests that \u03c4<\/code> could be used as a simple rating for comparing biofilters in low-TAN applications. If two filters are tested under comparable conditions, the filter with the higher \u03c4<\/code> removes more TAN per unit volume at the same TAN concentration.<\/p>\n

    For example, the authors note that a filter rated at \u03c4 = 1075 day-1<\/sup><\/code> would be more efficient on a media-volume basis than one rated at \u03c4 = 561 day-1<\/sup><\/code>. In simplified sizing terms, the higher-rated filter could require roughly half the volume of the lower-rated filter for the same low-TAN design goal.<\/p>\n

    This comparison is only valid when the testing conditions, media, water quality, and management approach are comparable. A \u03c4<\/code> value should not be treated as universal across species, salinities, loading regimes, or filter types.<\/p>\n

    A practical sizing relationship<\/h2>\n

    Once \u03c4<\/code> is known, the paper expresses TAN removal as:<\/p>\n

    Rate = \u03c4 A Vb<\/sub><\/span><\/p>\n

    And biofilter size as:<\/p>\n

    Vb<\/sub> = L(1 – Is<\/sub>) \/ (\u03c4 Ac<\/sub>)<\/span><\/p>\n

    Where Vb<\/code> is the biofilter volume used in the model, L<\/code> is TAN loading rate, Is<\/code> is the fraction of nitrification occurring in situ on tank and pipe surfaces, Ac<\/code> is the critical or target TAN concentration, and \u03c4<\/code> is the low-TAN normalized conversion capacity.[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.27.6″ _module_preset=”default” custom_padding=”20px|20px|20px|20px|false|false” border_radii=”on|16px|16px|16px|16px” border_width_all=”1px” border_color_all=”#d9e3e8″ border_width_left=”6px” border_color_left=”#7ab7a5″ global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_text _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n

    Design implication<\/h3>\n

    When the target TAN concentration is very low, biofilter volume can rise quickly. That is why low-range performance data is so important for hatchery and nursery systems.<\/p>\n

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    \n

    Suggested design workflow<\/h2>\n

    Use the linear approach as a focused low-TAN design tool, not as a universal biofilter model.<\/p>\n

      \n
    1. Define the TAN target.<\/strong> Set the maximum TAN concentration based on species, life stage, salinity, pH, temperature, and operational risk tolerance.<\/li>\n
    2. Use relevant low-TAN data.<\/strong> Estimate \u03c4<\/code> from performance data near the intended range, ideally between 0.1 and 0.5 g-TAN\/m3<\/sup> for the type of system discussed in the paper.<\/li>\n
    3. Avoid broad-range calibration when the system will run low.<\/strong> A curve fit dominated by higher TAN values may not protect the low-TAN target.<\/li>\n
    4. Account for organic loading.<\/strong> High BOD and solids accumulation can shift biofilm structure and reduce nitrification performance.<\/li>\n
    5. Size conservatively and verify.<\/strong> Use monitoring data after startup to confirm TAN and nitrite control under real feeding schedules.<\/li>\n
    6. Do not extrapolate blindly.<\/strong> The VTR = \u03c4A<\/code> relationship should not be extended into high-TAN or high-organic regimes without validation.<\/li>\n<\/ol>\n<\/section>\n
      \n

      When to use Monod, linear, or inhibition thinking<\/h2>\n\n\n\n\n\t\n\n\t\n\t\n\t
      Modeling approach<\/th>Best educational use<\/th>Main limitation<\/th>\n<\/tr>\n<\/thead>\n
      Monod \/ hyperbolic<\/td>Broad conceptual description of substrate-limited biofilter behavior.<\/td>Can be unstable when calibrated across contrasting regimes and does not represent high-organic collapse.<\/td>\n<\/tr>\n
      Direct linear regression<\/td>Practical low-TAN sizing and comparison in oligotrophic or mesotrophic systems.<\/td>Should be calibrated locally and not extrapolated to high loading.<\/td>\n<\/tr>\n
      Inhibition-style kinetics<\/td>Conceptual framework for biofilter performance loss under high organic loading.<\/td>The paper used this form for explanation and simulation, not as a final universal equation.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n<\/section>\n

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      Important cautions<\/h2>\n

      The paper does not say that Monod kinetics are useless. It says that for the specific goal of modeling low-TAN biofilter performance in oligotrophic and mesotrophic RAS, a simple local linear model may be more accurate and stable than a broadly calibrated Monod model.<\/p>\n

      The authors also call for additional field data. Their conclusion is strongest as an engineering recommendation for low-range calibration and as a warning against over-relying on peak carrying capacity when designing hatchery, broodstock, and nursery systems.<\/p>\n

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      Glossary<\/h2>\n

      A:<\/strong> TAN concentration in the bulk water.<\/p>\n

      Biofilter:<\/strong> A treatment unit that supports microbial communities that convert ammonia and nitrite in recirculating water.<\/p>\n

      Direct linear regression (DLR):<\/strong> A simple regression method used in the paper to fit VTR directly to TAN in the low-concentration range.<\/p>\n

      Heterotrophic interference:<\/strong> Reduced nitrification performance caused by heterotrophic bacteria competing for oxygen, space, or diffusion access in the biofilm.<\/p>\n

      Monod kinetics:<\/strong> A common model that describes substrate utilization as a curve approaching a maximum rate.<\/p>\n

      Oligotrophic:<\/strong> A low-nutrient, low-substrate condition. In this context, it refers to very low TAN targets in high-quality RAS water.<\/p>\n

      TAN:<\/strong> Total ammonia nitrogen, including ionized ammonium and unionized ammonia.<\/p>\n

      VTR:<\/strong> Volumetric TAN conversion rate, usually expressed as mass of TAN converted per biofilter volume per day.<\/p>\n

      \u03c4 (tau):<\/strong> The slope of the low-TAN linear relationship between TAN and VTR. In the paper, it serves as a normalized conversion capacity.<\/p>\n

      [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.27.6″ _module_preset=”default” background_color=”#e8f5f2″ custom_margin=”30px||||false|false” custom_padding=”20px|20px|20px|20px|false|false” border_radii=”on|30px|30px|30px|30px” border_width_all=”1px” border_color_all=”#d8d8d8″ global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_text module_id=”faq” _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n

      Frequently asked questions<\/h2>\n

      [\/et_pb_text][et_pb_accordion _builder_version=”4.27.6″ _module_preset=”default” toggle_level=”h4″ toggle_font=”|700|||||||” toggle_font_size=”16px” global_colors_info=”{}”][et_pb_accordion_item title=”Is the Monod model wrong?” open=”on” _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n

      No. The Monod model remains a useful conceptual and engineering tool. The issue is that a Monod curve calibrated across a broad operating range may not predict low-TAN performance well, especially when high organic loading changes biofilm behavior.<\/p>\n

      [\/et_pb_accordion_item][et_pb_accordion_item title=”Why does the paper focus on 0.1 to 0.5 g-TAN\/m3?” _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}” open=”off”]<\/p>\n

      That range reflects the oligotrophic and mesotrophic conditions relevant to broodstock, larval, and fingerling systems. It is also the range where low-TAN accuracy matters most for sensitive marine aquaculture applications.<\/p>\n

      [\/et_pb_accordion_item][et_pb_accordion_item title=”What does a higher \u03c4 value mean?” _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}” open=”off”]<\/p>\n

      A higher \u03c4<\/code> means the biofilter converts more TAN per unit volume at a given low TAN concentration. Under comparable conditions, a higher \u03c4<\/code> implies a smaller biofilter volume may be needed for the same TAN target.<\/p>\n

      [\/et_pb_accordion_item][et_pb_accordion_item title=”Can \u03c4 values be compared across all filters?” _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}” open=”off”]<\/p>\n

      Only with care. Comparisons should be made between filters tested under similar water quality, salinity, media, hydraulics, backwashing, loading, and operating conditions.<\/p>\n

      [\/et_pb_accordion_item][et_pb_accordion_item title=”Does the linear model predict filter collapse under high organic loading?” _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}” open=”off”]<\/p>\n

      No. The low-TAN linear model is not meant to describe high-load collapse. The paper argues that inhibition-style kinetics are needed to represent that behavior, while the linear approach is useful for the low-TAN design zone.<\/p>\n

      [\/et_pb_accordion_item][et_pb_accordion_item title=”What should operators monitor if they use this design logic?” _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}” open=”off”]<\/p>\n

      Operators should track TAN, nitrite, nitrate, dissolved oxygen, pH, alkalinity, feed rate, solids loading, and biofilter head loss or flow. The model is only one part of responsible system management.<\/p>\n

      [\/et_pb_accordion_item][\/et_pb_accordion][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_text _builder_version=”4.27.6″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n

      Source note<\/h2>\n

      This educational page summarizes and translates key concepts from: Malone, R.F., Bergeron, J., and Cristina, C.M. (2006). Linear versus Monod representation of ammonia oxidation rates in oligotrophic recirculating aquaculture systems<\/em>. Aquacultural Engineering<\/em>, 34, 214-223. DOI: 10.1016\/j.aquaeng.2005.08.005.<\/p>\n

      Editorial note: This page is written for education and content marketing. It should be paired with current engineering guidance, site-specific data, manufacturer specifications, species-specific water-quality targets, and professional review before being used for production design.<\/p>\n

      [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

      In low-TAN marine hatchery, broodstock, and fingerling systems, peak biofilter capacity is not always the most important design question. A simple linear model, calibrated only in the low-ammonia range, can be a more stable and practical way to estimate ammonia oxidation. Estimated read time: 8 minutes | Audience: aquaculture students, educators, RAS designers, hatchery teams, and water-quality professionals Educational summary adapted from Malone, Bergeron, and Cristina (2006), Linear versus Monod representation of ammonia oxidation rates in oligotrophic recirculating aquaculture systems.Key takeaways Low-TAN systems need a different design focus. Marine broodstock, larval, and fingerling systems often operate at very low total ammonia nitrogen (TAN), so low-range accuracy matters more than peak carrying capacity. A broadly calibrated Monod model can mislead low-TAN design. Monod kinetics are useful, but a single curve calibrated across high and low loading conditions may not accurately represent the oligotrophic range. Organic loading can suppress nitrification. As organic loading rises, fast-growing heterotrophic bacteria can interfere with nitrifiers and cause ammonia oxidation capacity to decline – a behavior the standard Monod curve does not represent. The paper supports a zero-intercept linear model for the low-TAN range. For TAN values around 0.1 to 0.5 g-TAN\/m3, the authors found that VTR […]<\/p>\n","protected":false},"featured_media":7438,"template":"","meta":{"_acf_changed":false,"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","inline_featured_image":false},"article_category":[40],"class_list":["post-7419","edu_article","type-edu_article","status-publish","has-post-thumbnail","hentry","article_category-filtration-system-design-sizing"],"acf":[],"yoast_head":"\nLinear vs. Monod Modeling for Ammonia Oxidation in Low-TAN RAS - Aquatic Systems<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/astfilters.com\/aquatic-systems\/articles\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Linear vs. Monod Modeling for Ammonia Oxidation in Low-TAN RAS - Aquatic Systems\" \/>\n<meta property=\"og:description\" content=\"In low-TAN marine hatchery, broodstock, and fingerling systems, peak biofilter capacity is not always the most important design question. A simple linear model, calibrated only in the low-ammonia range, can be a more stable and practical way to estimate ammonia oxidation. Estimated read time: 8 minutes | Audience: aquaculture students, educators, RAS designers, hatchery teams, and water-quality professionals Educational summary adapted from Malone, Bergeron, and Cristina (2006), Linear versus Monod representation of ammonia oxidation rates in oligotrophic recirculating aquaculture systems.Key takeaways Low-TAN systems need a different design focus. Marine broodstock, larval, and fingerling systems often operate at very low total ammonia nitrogen (TAN), so low-range accuracy matters more than peak carrying capacity. A broadly calibrated Monod model can mislead low-TAN design. Monod kinetics are useful, but a single curve calibrated across high and low loading conditions may not accurately represent the oligotrophic range. Organic loading can suppress nitrification. As organic loading rises, fast-growing heterotrophic bacteria can interfere with nitrifiers and cause ammonia oxidation capacity to decline - a behavior the standard Monod curve does not represent. The paper supports a zero-intercept linear model for the low-TAN range. For TAN values around 0.1 to 0.5 g-TAN\/m3, the authors found that VTR […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/astfilters.com\/aquatic-systems\/articles\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras\/\" \/>\n<meta property=\"og:site_name\" content=\"Aquatic Systems\" \/>\n<meta property=\"article:modified_time\" content=\"2026-06-16T15:17:49+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/astfilters.com\/aquatic-systems\/wp-content\/uploads\/sites\/3\/2026\/06\/broodstock-facility.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1000\" \/>\n\t<meta property=\"og:image:height\" content=\"500\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"10 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/articles\\\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras\\\/\",\"url\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/articles\\\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras\\\/\",\"name\":\"Linear vs. Monod Modeling for Ammonia Oxidation in Low-TAN RAS - Aquatic Systems\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/articles\\\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/articles\\\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/wp-content\\\/uploads\\\/sites\\\/3\\\/2026\\\/06\\\/broodstock-facility.jpg\",\"datePublished\":\"2026-06-16T15:14:43+00:00\",\"dateModified\":\"2026-06-16T15:17:49+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/articles\\\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/articles\\\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/articles\\\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras\\\/#primaryimage\",\"url\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/wp-content\\\/uploads\\\/sites\\\/3\\\/2026\\\/06\\\/broodstock-facility.jpg\",\"contentUrl\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/wp-content\\\/uploads\\\/sites\\\/3\\\/2026\\\/06\\\/broodstock-facility.jpg\",\"width\":1000,\"height\":500},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/articles\\\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Educational Articles\",\"item\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/articles\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Linear vs. Monod Modeling for Ammonia Oxidation in Low-TAN RAS\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/#website\",\"url\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/\",\"name\":\"Aquatic Systems\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/astfilters.com\\\/aquatic-systems\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Linear vs. Monod Modeling for Ammonia Oxidation in Low-TAN RAS - Aquatic Systems","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/astfilters.com\/aquatic-systems\/articles\/linear-vs-monod-modeling-for-ammonia-oxidation-in-low-tan-ras\/","og_locale":"en_US","og_type":"article","og_title":"Linear vs. Monod Modeling for Ammonia Oxidation in Low-TAN RAS - Aquatic Systems","og_description":"In low-TAN marine hatchery, broodstock, and fingerling systems, peak biofilter capacity is not always the most important design question. A simple linear model, calibrated only in the low-ammonia range, can be a more stable and practical way to estimate ammonia oxidation. Estimated read time: 8 minutes | Audience: aquaculture students, educators, RAS designers, hatchery teams, and water-quality professionals Educational summary adapted from Malone, Bergeron, and Cristina (2006), Linear versus Monod representation of ammonia oxidation rates in oligotrophic recirculating aquaculture systems.Key takeaways Low-TAN systems need a different design focus. Marine broodstock, larval, and fingerling systems often operate at very low total ammonia nitrogen (TAN), so low-range accuracy matters more than peak carrying capacity. A broadly calibrated Monod model can mislead low-TAN design. Monod kinetics are useful, but a single curve calibrated across high and low loading conditions may not accurately represent the oligotrophic range. Organic loading can suppress nitrification. As organic loading rises, fast-growing heterotrophic bacteria can interfere with nitrifiers and cause ammonia oxidation capacity to decline - a behavior the standard Monod curve does not represent. The paper supports a zero-intercept linear model for the low-TAN range. 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