Nutrient delivery ratio

Fertilizer on soybean fields, dung on pasture and sewage from towns put nitrogen and phosphorus into the water, where they feed algae, use up the oxygen fish need and make drinking water harder and more expensive to treat. Part of these nutrients never reaches a river: on the way down, the soil, the roots and the leaf litter of forest, grassland and wetlands take them up or hold them. That retention is an ecosystem service, and strips of forest along the rivers are the classic way to restore it. InVEST's nutrient delivery ratio (NDR) model maps both sides: how much nitrogen and phosphorus each land use releases, and how much of it reaches a stream. In this tutorial you will build it in Terraflux on Ribeirão Claro, read its maps of retention, delivery and export, learn which settings move the answer, and see why the riparian restoration of the 2040 scenario cuts the surface export of nitrogen while the subsurface export still rises.

The idea#

The model follows a nutrient from the cell where it is released to the first stream below it, in three steps.

How much each cell releases. Each land use class gets a load: kilograms of nitrogen and of phosphorus per hectare and year. Usually these are export coefficients, the loads measured at the edge of fields, pastures or forests in studies of small catchments. Wetter places wash out more, so the load of each cell is scaled by a runoff proxy: annual rain, or a quickflow index, divided by its mean over the landscape. For nitrogen, part of the load dissolves and travels down through the soil instead of over it.

How much the land below retains. Every class also has a retention efficiency \(\text{eff}_j\) (0 to 1), the largest share of the nutrients passing through it that it can retain, and a critical length \(\ell_j\) (m), the distance over which it reaches that share. Natural vegetation retains much (InVEST's guide gives above 0.8 as typical), a road or a town almost nothing. The load of a cell crosses the cells below it on its way to the stream, and the model accumulates their retention into an effective retention \(\text{eff}'\), from the stream up:

The third case is the one to notice: a cell that retains less than the land below it takes the retention of that land. A soybean field above a strip of forest is credited with the strip's retention, because its nutrients have to cross the strip.

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How well a cell is connected to the stream. As in the sediment model, the share that reaches a stream also depends on the terrain: the index of connectivity of Borselli et al. (2008) is high for cells that drain a large, steep area and lie close to the stream, low for cells far from it behind long gentle slopes. The model turns it into a delivery ratio with the sigmoid that Vigiak et al. (2012) used for sediment, scaled down by the effective retention:

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The subsurface path. The dissolved nitrogen of the subsurface load is retained by the soil according to the distance alone, the same for every land use:

A worked cell: cropland on rain equal to the mean (\(\text{RPI} = 1\)), 300 m from the stream along the flow (about the median of Ribeirão Claro), with an index of connectivity of \(-2\) (about the landscape's mean). Its 20 kg of nitrogen split into 12 kg over the surface and 8 kg through the soil. Without forest below it, \(\text{eff}' = 0.15\) and \(NDR = 0.85 / (1 + e^{(-1.18 + 2)/2}) = 0.34\): 4.1 kg reach the stream over the surface. Above the forest strip of the figure, \(\text{eff}' = 0.76\), \(NDR = 0.096\) and only 1.1 kg do. Through the soil, \(NDR_{\text{subs}} = 1 - 0.8\,(1 - e^{-5 \times 300/200}) = 0.20\): 1.6 kg, with or without the strip.

When to use it#

• Where to restore: the cells whose vegetation keeps the most nutrients out of the rivers, and the riparian strips that would retain most if restored.
• Scenarios: how much more nitrogen and phosphorus reach a reservoir if pasture becomes cropland, or less if the riparian forest the Brazilian Forest Code requires along rivers is restored.
• Water funds and payments for watershed services that target the farms upstream of a water intake.
• Which classes are the sources, for a plan of fertilizer management or of livestock.

What it is not: the model works with annual averages of diffuse sources. It has no in-stream processes (no uptake or deposition in the channel, no retention in reservoirs), no point sources (the sewage of the town is not in it unless you add it), no seasons or storms, and no lag of nitrogen in the groundwater, which can take years or decades to reach a river. It gives loads (kg / yr), not concentrations. InVEST's guide warns that the outputs are highly sensitive to the inputs, above all to the loads, and that calibration is difficult; use the model to compare places and scenarios, and the absolute numbers with care. Phosphorus travels mostly bound to soil particles, so read its export with the sediment model beside it. For daily flows and water quality with in-stream processes, use a process model such as SWAT+ (swat.run).

What you need#

All rasters on the grid of the land use map, projected in metres:

The model fills the DEM's depressions and routes the flow over it, and runs only inside the watersheds (polygons without ws_id are numbered 1, 2...).

Ribeirão Claro's files are in ribeirao-claro.zip; the nutrient table, which the other parts do not use, is in ribeirao-claro-ndr.zip. The runoff proxy here is the annual rain, as InVEST's guide allows when no quickflow index is at hand; services.seasonal_water_yield computes one.

The biophysical table, by class (lucode): for nitrogen load_n (kg / ha / yr), eff_n (0 to 1), crit_len_n (m) and proportion_subsurface_n (0 to 1); for phosphorus load_p, eff_p and crit_len_p. The values here are illustrative, chosen to be plausible for the land uses of the Cerrado and the Atlantic forest (fertilized soybean and maize, extensive cattle pasture, native forest, eucalyptus); use measured export coefficients and retention efficiencies for your region:

and, in the same table, phosphorus:

The loads are measured runoff (export coefficients), Terraflux's default. The critical lengths follow InVEST's guide, which reports 10 to 300 m from the literature on riparian buffers and suggests 150 m as a start (and the size of a cell where nothing is known); here forest has 150 m, and cropland and the town the size of a cell. In InVEST the load types are columns of the table (load_type_n, load_type_p); in Terraflux they are settings of the node (below). For the subsurface path the tutorial uses the global averages the guide suggests after Mayer et al. (2007): a critical length of 200 m and an efficiency of 0.8.

Build the model#

format = "terraflux/1"

[[nodes]]
id = "dem"
op = "raster.read"
params = { path = "dem.tif" }

[[nodes]]
id = "lulc"
op = "raster.read"
params = { path = "lulc_2020.tif" }

[[nodes]]
id = "rain"
op = "raster.read"
params = { path = "precipitation.tif" }
note = "The runoff proxy."

[[nodes]]
id = "biophysical"
op = "table.read"
params = { path = "biophysical_ndr.csv" }
note = "Loads, efficiencies, critical lengths."

[[nodes]]
id = "watersheds"
op = "vector.read"
params = { path = "watersheds.gpkg" }

[[nodes]]
id = "nutrients"
op = "services.ndr"
inputs = { dem = "dem.raster", lulc = "lulc.raster", runoff_proxy = "rain.raster", biophysical = "biophysical.table", watersheds = "watersheds.vector" }
params = { threshold = 1000, k = 2, subsurface_critical_length = 200, subsurface_efficiency = 0.8, method = "mfd" }

Behind the node, the chain is InVEST's: the DEM's depressions filled, the flow routed by multiple flow directions (mfd, the default: each cell's water split among its lower neighbours, as pygeoprocessing does) or by d8 (all of it to the steepest neighbour), the flow accumulated, the streams traced, the slope, the index of connectivity, the effective retention, the delivery ratios and the exports. Its outputs:

Terraflux's node is InVEST 3.20's model, run through landschaft's port of it. landschaft's tests run InVEST 3.20.2 on synthetic landscapes (with multiple flow directions and D8, nitrogen and phosphorus) and require every raster of the chain to hold the same 32-bit numbers (on Windows), and the watershed totals to agree to float32 precision; Terraflux's tests require its maps to be landschaft's to the bit. One difference is deliberate: InVEST 3.20 measures the distance to the stream of the subsurface delivery in cells but compares it with a critical length in metres; Terraflux, like landschaft, measures it in metres (cells times the cell size). To reproduce a run of InVEST exactly, give Terraflux InVEST's critical length times the cell size (6,000 for InVEST's 200 on cells of 30 m).

Loads given as application rates#

If your table holds the fertilizer or manure applied rather than measured export, set load_type_n (and load_type_p) to "application-rate": the model then multiplies each load by \(1 - \text{eff}\) of its class before scaling it. Mixed tables are allowed in the model file, with one type per class code:

format = "terraflux/1"

[[nodes]]
id = "nutrients"
op = "services.ndr"
inputs = { dem = "dem.raster", lulc = "lulc.raster", runoff_proxy = "rain.raster", biophysical = "biophysical.table", watersheds = "watersheds.vector" }
params = { threshold = 1000, subsurface_critical_length = 200, subsurface_efficiency = 0.8, load_type_n = { "1" = "measured-runoff", "2" = "measured-runoff", "3" = "application-rate", "4" = "measured-runoff", "5" = "measured-runoff", "6" = "measured-runoff" } }

Cropland's 20 kg then count as 17 kg (\(20 \times (1 - 0.15)\)), and the nitrogen export of the two watersheds falls from 4,134 to 3,843 kg / yr. Every class needs its type when you give them by class.

Read the results#

Retention and delivery#

The effective retention is the map of the service: high where the land retains, and downslope of where it retains. The forest on the ridges retains what it releases; the forest on the lower slopes also retains what the fields above it release. Most of the landscape delivers less than 20% of its surface load (mean NDR 0.15); the cells next to the streams, well connected and with little land below them, deliver up to 73%.

Export#

One thing to know about the table: its total export is less than the sum of the surface and subsurface exports (in watershed 1, \(1\,396 + 1\,087 = 2\,483\), not \(2\,334\) kg). The stream cells have a subsurface export but no surface export, so no total either; their subsurface export (248 kg a year in the two watersheds) is in the column n_subsurface_export and not in n_total_export. InVEST's own results have the same gap. Report the columns you used.

Which classes send the nutrients?

The scenario of 2040#

Run the same model with lulc_2040.tif. The scenario clears forest edges, turns pasture into cropland, grows the town, and restores the pasture and cropland along the rivers to forest.

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2020

2040

The loads rise by a quarter to two fifths, yet the surface export of nitrogen falls by 10% and that of phosphorus barely moves: the riparian forest retains the extra load and more. The subsurface export of nitrogen rises with its load (+23%), because the model's soil retains dissolved nitrogen by distance alone, whatever grows on it. So the total nitrogen export still rises by 8%. Two lessons: a riparian strip in this model works on the surface path only, and how much nitrogen you assign to the subsurface (proportion_subsurface_n) can decide whether a scenario looks better or worse. The index of connectivity is the same in both years (it does not depend on the land use); everything that changes comes from the loads and the retention.

Settings that change the answer#

The stream threshold#

The threshold decides where hillslopes end and streams begin. A smaller threshold draws more streams, so every cell is closer to one, better connected, and has less land below it to retain its load:

Enlarge

PlayStream threshold (cells)

Choose the threshold so that the streams match a map of the real rivers, not to reach a number. With the same threshold the NDR draws fewer stream cells than the sediment model (81 ha against 99 ha at 1,000 cells here): InVEST's two models trace the streams from multiple flow directions with different settings, and Terraflux follows each.

Borselli's k#

The effect is much smaller than in the sediment model, where \(k\) changed the export by a factor of a thousand. Here \(IC_0\) sits in the middle of the landscape's indices, so cells lie on both sides of the curve: a larger \(k\) raises the delivery of the poorly connected cells and lowers that of the well connected ones, and the two partly cancel. Keep InVEST's default (2) unless measured loads give you a reason to change it.

The critical lengths#

How far the vegetation must extend to reach its efficiency matters less than the efficiency itself. Multiplying every class's critical length by the same factor:

The subsurface path#

These two numbers are among the least known of the model. Without local data, keep the guide's averages, and show the reader how the answer changes over a plausible range.

Multiple flow directions or D8#

Common pitfalls#

• Loads, their units and their type. Loads are in kg per hectare and year. Export coefficients are measured runoff (the default); fertilizer and manure applied are application rates (load_type_n, load_type_p). Mixing them up changes the load by the factor \(1 - \text{eff}\).
• Comparing runs of different extents. Both the runoff proxy's mean and \(IC_0\) are computed over the cells of the run. Clip the landscape differently, add a watershed or change the threshold, and every cell's load and delivery ratio change. Compare scenarios on the same DEM, watersheds and threshold; to keep the proxy's scaling fixed between runs, give runoff_proxy_mean.
• Reading the watershed total as the sum of its parts. n_total_export leaves out the subsurface export of the stream cells (above).
• The streams have no surface export. The surface load of a stream cell, and the delivery ratio, are missing there, as in InVEST: give the water class a load of 0, and check that the streams of the model match the rivers.
• The subsurface distance. In metres in Terraflux, in cells in InVEST 3.20 (above): a critical length copied from a study that used InVEST may need the cell size.
• Point sources and in-stream processes. The town's sewage, a feedlot or a fish farm are not in the land use loads; reservoirs and wetlands on the river retain nutrients the model does not see. Add point sources to the watershed totals yourself, and do not read the export as the load at the outlet.
• The resolution. The connectivity and the retention paths come from the DEM: a 90 m grid has other paths and other strips than a 30 m one (InVEST's guide notes that the effect of resolution on the model has not been well studied). Narrow riparian strips need fine cells to exist at all.
• Phosphorus without sediment. The model routes phosphorus like nitrogen's surface part; most phosphorus leaves attached to eroded soil. Compare with the sediment export.

Going further#

• Ecosystem service models: the ideas for what the series' models have in common, and Ribeirão Claro.
• Sediment delivery ratio, the same connectivity applied to soil.
• Annual water yield on the same watersheds, and Seasonal water yield, the next part, whose quickflow is the runoff proxy InVEST recommends.
• Monte Carlo uncertainty to carry the uncertainty of the loads and efficiencies into the export.
• The operators' reference: services.ndr, services.seasonal_water_yield (a quickflow index for the runoff proxy), hydro.watersheds.

References#

• Borselli, L., Cassi, P., & Torri, D. (2008). Prolegomena to sediment and flow connectivity in the landscape: A GIS and field numerical assessment. Catena, 75(3), 268–277. https://doi.org/10.1016/j.catena.2008.07.006
• Mayer, P. M., Reynolds, S. K., McCutchen, M. D., & Canfield, T. J. (2007). Meta-analysis of nitrogen removal in riparian buffers. Journal of Environmental Quality, 36(4), 1172–1180. https://doi.org/10.2134/jeq2006.0462
• Natural Capital Alliance. (2026). InVEST 3.20.2 User's Guide: NDR, nutrient delivery ratio. https://storage.googleapis.com/releases.naturalcapitalproject.org/invest-userguide/latest/en/ndr.html
• Redhead, J. W., May, L., Oliver, T. H., Hamel, P., Sharp, R., & Bullock, J. M. (2018). National scale evaluation of the InVEST nutrient retention model in the United Kingdom. Science of the Total Environment, 610–611, 666–677. https://doi.org/10.1016/j.scitotenv.2017.08.092
• Valladares-Castellanos, M., de Jesús Crespo, R., Xu, Y. J., & Douthat, T. H. (2024). A framework for validating watershed ecosystem service models in the United States using long-term water quality data: Applications with the InVEST Nutrient Delivery (NDR) model in Puerto Rico. Science of the Total Environment, 949, 175111. https://doi.org/10.1016/j.scitotenv.2024.175111
• Vigiak, O., Borselli, L., Newham, L. T. H., McInnes, J., & Roberts, A. M. (2012). Comparison of conceptual landscape metrics to define hillslope-scale sediment delivery ratio. Geomorphology, 138(1), 74–88. https://doi.org/10.1016/j.geomorph.2011.08.026