dorsal/arxiv
View SchemaSolution of a Model for the Oceanic Pycnocline Depth: Scaling of Overturning Strength and Meridional Pressure Difference
| Authors | Anders Levermann, Alexa Griesel |
|---|---|
| Categories | |
| ArXiv ID | physics/0408061 |
| URL | https://arxiv.org/abs/physics/0408061 |
| DOI | 10.1029/2004GL020678 |
Abstract
We present an analysis of the model by Gnanadesikan [1999] for the pycnocline depth in the ocean. An analytic solution for the overturning strength as a function of the meridional pressure difference is derived and used to discuss their mutual scaling. We show that scaling occurs only in two unphysical regimes of the model. In the absence of the Southern Ocean (SO) processes, i.e. for a northern overturning cell, the volume transport is proportional to the square root of the pressure difference. Linear scaling is seen when the overturning is restricted entirely to the SO, i.e. when no northern downwelling exists. For comparison, we present simulations with the coupled climate model CLIMBER-3$\alpha$ which show linear scaling over a large regime of pressure differences in the North Atlantic (NA). We conclude that the pycnocline model is not able to reproduce the linear scaling between its two central variables, pressure and volume transport.
{
"annotation_id": "2c2fc2d0-e92c-4dd6-a12c-66b741072b3b",
"date_created": "2026-03-02T18:00:53.360000Z",
"date_modified": "2026-03-02T18:00:53.360000Z",
"file_hash": "e7c6aca02d8eb2077327c2c2aae69f2d38468f7bc1a7063d0f64554d70bcf174",
"private": false,
"record": {
"abstract": "We present an analysis of the model by Gnanadesikan [1999] for the pycnocline\ndepth in the ocean. An analytic solution for the overturning strength as a\nfunction of the meridional pressure difference is derived and used to discuss\ntheir mutual scaling. We show that scaling occurs only in two unphysical\nregimes of the model. In the absence of the Southern Ocean (SO) processes, i.e.\nfor a northern overturning cell, the volume transport is proportional to the\nsquare root of the pressure difference. Linear scaling is seen when the\noverturning is restricted entirely to the SO, i.e. when no northern downwelling\nexists. For comparison, we present simulations with the coupled climate model\nCLIMBER-3$\\alpha$ which show linear scaling over a large regime of pressure\ndifferences in the North Atlantic (NA). We conclude that the pycnocline model\nis not able to reproduce the linear scaling between its two central variables,\npressure and volume transport.",
"arxiv_id": "physics/0408061",
"authors": [
"Anders Levermann",
"Alexa Griesel"
],
"categories": [
"physics.ao-ph",
"physics.geo-ph"
],
"doi": "10.1029/2004GL020678",
"title": "Solution of a Model for the Oceanic Pycnocline Depth: Scaling of Overturning Strength and Meridional Pressure Difference",
"url": "https://arxiv.org/abs/physics/0408061"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "96c844ad-325d-4e86-8ec6-172e3c3d0535",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}