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The tropopause is a transitional layer between the troposphere and the stratosphere. The exchange of chemical constituents of the atmosphere (namely masses of air, water vapor, trace gases etc.) and energy between the troposphere and the stratosphere occurs through this layer. We suppose that just exchanges that are taking place at the tropopause heights are strongly influenced by the Global Change forcing. For this reason it is particularly urgent to accumulate temporal data the most accurate possible and with a certain continuity series to understand comprehensively what is happening to our climate. It is well known that Radio Occultation technique applied using Global Navigations Satellite Systems (GNSS-RO) is a powerful tool to detect the tropopause heights. It can be done working on the level 2 data provided by GNSS-RO payload:
* i.e.* atmospheric profiles of pressure and temperature. We propose to measure tropopause using GNSS-RO level 1 data;
*i.e.* the bending angles (BA) of the GNSS signal through the atmosphere. We fit the BA profiles applying in the integral relationship of BA as refractivity profile of background the Hopfield dry model of atmosphere which depends on the fourth degree of the height above the Earth. Through the layers in which tropopause is contained, the residuals between the background model and the observed BA have an anomalous trend. The residuals in this zone form anomalous non-gaussian bumps that we have exploited just to determine the relevant parameters of the tropopause. Such bumps are due to the wrong theoretical assumption made by Hopfield for the re-construction of the dry refractivity that the temperature lapse rate of the atmosphere is constant. But we know that the definition of tropopause according the World Meteorological Organization (WMO) is just the height where a sudden change of the temperature lapse rate usually occurs. Thus in the present work we have determined tropopause heights with new algorithms which exploit the bumps occurring along the BA profiles achieved by GNSS-RO. We have used the huge amount of data provided by several space missions devoted to GNSS-RO (namely COSMIC, METOP, etc.) for tuning the algorithms, performed a validation and provided a robust statistical soundness. The same GNSS-RO observations are helpful also to reconstruct the Mapping Function commonly applied in geodetic applications. Global mapping functions built with GNSS-RO and their evolution in time can be an interesting parameter helpful for climate investigations as well.

In 1996, the Intergovernmental Panel on Climate Change (IPCC) [

It is well known as signals of Global Change are given not only by Earth’s temperatures but also by a wide variety of other parameters such as the integrated heat content [

One of the temperature-free variables that has not been still fully exploited for climate change investigations is height of the tropopause [_{2}O vapour has an important role in the Earth’s radiative balance and in stratospheric chemistry [_{2}O vapour causes the troposphere to warm, the stratosphere to cool [_{3} loss [

While moisture-rich air masses are transported through this region, most water vapour condenses resulting in extremely dry lower stratospheric air. Thus H_{2}O abundance varies seasonally as well as the tropopause temperature does. Other possible causes can be a direct injection of H_{2}O vapour due to overshooting convection mechanism as well as oxidation of methane within the stratosphere [_{2}O vapour showed significant long-term variability and an upward trend over the last half of the 20th century, but no net increase since 1996”. In fact, the latest observations confirm inter-annual variations but not significant secular trends since 1996. The minimum temperature that marks the tropopause, wringing water out of the tropospheric air; thus any air reaching the stratosphere from below contains very little water vapour. The vertical temperature structure in the vicinity of the tropopause controls static stability and, therefore, determines where and how deeply air will penetrate into stratosphere from below.

In the last decades the structure of global tropopause has been studied mainly with radiosonde observations (RAOB) and reanalysis data from Numerical Weather Prediction (NWP) models provided by the European Centre for Medium Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP). The tropopause reacts to other factors as well: variations in solar radiation, atmospheric angular momentum, stratospheric ozone and, last but not least, to the explosive volcanic eruptions. The observations have identified decadal-timescale changes in tropopause height as explained in [

Studies since the 5th IPCC report [

In the last decade a huge number of GNSS RO data have opened very promising perspectives for a more refined monitoring of tropopause heights which, for all the above considerations done, revealed to be a powerful fingerprint for climate investigations. GNSS RO indeed have been widely demonstrated the capability to retrieve the temperature and the height of the tropopause within an error of 1 K and few hundreds of meters respectively as predicted in [

In the period from 2006 Sept. to 2009-Sept the variation of tropopause heights increased over the North polar area and in the equatorial bulge. The average trend in the equatorial bulge is of 1.4 m/yr but in the restricted zonal 12N-12S its value is at a level of 2.2 m/yr. These observations performed with RO data confirm the trend experienced since 1978 about the rising of the tropopause cold point level by 20 m per decade, cooling by 0.5 K per decade, and decrease in pressure by 0.5 hPa per decade through the equatorial bulge.

After having provided a wide and deep frame of how tropopause can be considered a key parameter for climate investigation, in the first section of the present work we will describe how currently the tropopause heights are determined. It will explain in particular the method to determine the Radio Tropopause by GNSS-RO as proposed in [

Global Trend | 0.1 m/yr | Increasing! |
---|---|---|

60N-90N | 11.1 m/yr | |

24N-60N | −3.1 m/yr | |

18N-18S | 1.4 m/yr | 2.2 m/yr (12N-12S) |

24S-60S | −0.8 m/yr | |

60S-90S | −2.5 m/yr |

algorithm we propose to determine the tropopause by GNSS-RO. Afterward we will show the results of validation performed.

In the 4th section we will propose a new possible key parameter, suitable to perform climate investigations: i.e. the Mapping Function built with GNSS-RO observations. Finally some conclusions and remarks will be drawn.

The World Meteorological Organization (WMO) in 1957 provided a definition of MTs based on lapse rate tropopause (LRT), which until now is the only available way to detect MTs: “The lowest level at which the lapse rate decreases to 2 C/km or less, provided that the average lapse rate between this level and all higher levels within 2 km does not exceed 2 C/km.” Using this definition and realizing the importance of the tropopause structure for climate investigations as extensively explained before, many investigators have studied the LRT using GNSS RO measurements [

where

We propose the BPV approach to retrieve humidity profile from GNSS RO observations without using external information [

In the first step we adopt the Hopfield dry atmosphere refractivity model [

The parameters of Hf, surface pressure and temperature P_{0} and T_{0}, are estimated by a Levenberg-Marquardt non-linear fit applied to the cost function as written in Equation (2).

where γ_{obs} are the observed bending angles, _{E} is the Earth radius, h_{max} is the upper bound of ray tracing integration (namely stratopause) a is the impact parameter.

_{dry}_{,0} is the ground dry refractivity _{dry} is the Hf stratopause height [

In the second step, from the estimated parameters T_{0} and P_{0}, the dry BA is computed down to the ground by applying the dry Hf model. In _{max} where we have the maximum value of the residuals (blue square); H_{0} where the residuals start to be negative soon after H_{max} (green square); H_{min} where the residual is minimum (gray square).

We have performed a validation of the proposed tropopause gauges using both GNSS RO and Radiosondes observations (RAOB). In particular we have computed in turn the CPT (h_{CPT}) and LRT (h_{LRT}) with GNSS-RO and the same parameters with RAOB (h_{CPT-RAOB}, h_{LRT-RAOB )}. In addition we have computed the Radio Tropopause (h_{RT}) applying its definition just as conceived in [

They are capable of retrieving about 2000 of GNSS-RO events/day. The satellites have onboard receivers with a high gain antenna and open-loop tracking channels [

In _{ave} and H_{max} represent quite well the LRT (see yellow boxes of the tables). The agrement is particularly outstanding with LRT computed with RAOB (hLRT- RAOB) which is well within the vertical resolution of GNSS-RO! The agreement with H_{max} seems slightly preferable but its scatter (see the II frame of _{0} is closer to the Cold Point Tropopause (CPT. h_{CPT} and h_{CPT-RAOB}) and to the Radio Tropopause (RT, hRT). Also in this case the agreement with RAOB data is preferable. The main drawback is represented by the really high values of the scatter which could make unwise replace the CPT points with H_{0}. The validation of the RT [_{0} and h_{RT} are indeed very close to those with h_{CPT}. The scatter of h_{RT} (not shown in _{CPT} and h_{CPT-RAOB} is in turn of about 0.75 and 1.05 km.

h_{CPT} | h_{CPT-RAOB} | h_{LRT} | h_{LRT-RAOB} | h_{RT} | |
---|---|---|---|---|---|

H_{ave} | −0.990 | −1.275 | −0.275 | −0.147 | −1.122 |

H_{max} | −0.918 | −1.224 | −0.235 | −0.143 | −1.070 |

H_{0} | 0.711 | 0.365 | 1.654 | 1.726 | 0.677 |

H_{min} | 2.848 | 2.535 | 3.643 | 3.668 | 2.659 |

h_{CPT} | h_{CPT-RAOB} | h_{LRT} | h_{LRT-RAOB} | h_{RT} | |

H_{ave} | 1.565 | 1.813 | 0.851 | 0.858 | 1.915 |

H_{max} | 1.601 | 1.874 | 0.994 | 1.087 | 1.970 |

H_{0} | 1.759 | 1.773 | 1.984 | 2.091 | 1.963 |

H_{min} | 3.370 | 3.178 | 3.858 | 3.869 | 3.135 |

The GNSS signal arrives to the receiver from a direction that forms an arbitrary angle with the zenith direction. Thus the most convenient way to model the TD is to express it as the product of the ZTD and a Mapping Function (hereafter MF). The MF is essentially a slant factor which provides the number of air masses crossed by the signal through the atmosphere as a function of the elevation angle E. MF = 1 for the zenith direction; while MF = 1/Sin(E) for other directions, assuming the layers of the atmosphere flat. But the atmosphere layers are not flat! Thus it was proposed in [

The coefficients involved in Equation (3) were initially retrieved with RAOB with coefficients as function of some atmospheric parameters such as latitude, the Day Of the Year (DOY) and heights [

In the last years it was proposed to use directly the values of pressure, humidity and temperature provided by climatological (the Global Mapping Function: GMF) and/or Numerical Weather Prediction (the Vienna Mapping Function: VMF_1) models as in [

In our case the big number of GNSS-RO observations collected up to now have allowed us to extend the computation of harmonic up to the 18th degree instead of 8th as in [

It is currently well known the relevance of the tropopause as a fingerprint to study atmospheric Global Change. The huge availability of GNSS RO data thanks to missions like COSMIC or METOP, have made its measurements on global scale easier and more precise. Furthermore it has been realized that atmospheric profiles other than temperature ones, e.g. refractivity or BA, could make still easier and more precise the measurement of tropopause height. In the present paper we have proposed indeed a new method to determine the tropopause. The method we have proposed fits the BA profiles assuming Hf as refractivity dry model. The model was built [_{ave}, H_{max}, H_{0} andH_{min}. The first 2 parameters have revealed to be very close to the LRT; while H_{0} is closer to the CPT. The activity developed have also provided, as by product, the validation of the Radio Tropopause [

Vespe, F., Pacione, R. and Rosciano, E. (2017) A Novel Tool for the Determination of Tropopause Heights by Using GNSS Radio Occultation Data. Atmospheric and Climate Sciences, 7, 301- 313. http://dx.doi.org/10.4236/acs.2017.73022