A comparison of low-level wind profiles from Mode-S EHS data with ground-based remote sensing data

Abstract

The Romanian Air Traffic Services Administration is currently testing the operational production of vertical wind profiles calculated from aircraft-reported Mode-Select enhanced surveillance (EHS) data provided by secondary surveillance radars. This paper presents an estimation and a verification of the biases of the calculated wind components using a reference represented by sodar and lidar measured wind. The biases are caused by errors in the magnetic declination, neglecting the pitch angle of aircraft in the initial climb, and by errors of sodar or lidar orientation. The estimated bias of the meridional components confirms the flight direction dependence of the error of wind components transversal to the flight track found in previous studies, while the strong correlation of wind and flight direction in aerodrome traffic makes this bias to cause a bias of the wind direction more evident at low wind speeds (≃ 10°). The estimated zonal component bias is negligible with descending aircraft, but positive, depending on the pitch angle, up to approximately 50% of the component, with ascending aircraft. The verification of the accuracy of these estimates is performed by comparing the ground-based remote-sensed wind data with the Mode-S EHS derived wind data in the lower boundary layer of Bucharest Henri Coanda airport area. Results show a generally good agreement with the predictions of the measurement error model, with residual errors being assigned to intrinsic instrument measurement errors and assumptions on the average aircraft speed.

Appendices

Appendix 1

Using the first order Taylor series expansion of function (u, v) (α, β, γ) about the point $(\alpha_{0} ,\beta_{0} ,\gamma_{0} )$, we obtain a first order estimate the effect of small errors of the variables (α, β, γ) on (u, v), in the vicinity of the point $\left( {\alpha_{0} ,\beta_{0} ,\gamma_{0} } \right)$:

$$\delta \left( {u,v} \right)\left( {\alpha_{0} ,\beta_{0} ,\gamma_{0} } \right) = \left( {u,v} \right)\left( {\alpha_{0} + \delta \alpha ,\beta_{0} + \delta \beta ,\gamma_{0} + \delta \gamma } \right) - \left( {u,v} \right)\left( {\alpha_{0} ,\beta_{0} ,\gamma_{0} } \right) = \frac{{\partial \left( {u,v} \right)}}{\partial \alpha }\left( {\alpha_{0} ,\beta_{0} ,\gamma_{0} } \right) \cdot \delta \alpha + \frac{{\partial \left( {u,v} \right)}}{\partial \beta }\left( {\alpha_{0} ,\beta_{0} ,\gamma_{0} } \right) \cdot \delta \beta + \frac{{\partial \left( {u,v} \right)}}{\partial \gamma }\left( {\alpha_{0} ,\beta_{0} ,\gamma_{0} } \right) \cdot \delta \gamma$$

(27)

From (4) and (5) we calculate the derivatives of u and v with respect to α, β, γ and approximating cos α = 0, sin α =  + 1/− 1 for α = 80°/260°, we obtain:

$$\frac{\partial u}{{\partial \alpha }} = 0$$

(28)

$$\frac{\partial v}{{\partial \alpha }}\left( {\alpha = 80} \right) = - V_{{\text{g}}}$$

(29)

$$\frac{\partial v}{{\partial \alpha }}\left( {\alpha = 260} \right) = - V_{{\text{g}}}$$

(30)

$$\frac{\partial u}{{\partial \beta }} = v$$

(31)

$$\frac{\partial v}{{\partial \beta }}\left( {\alpha = 260^\circ } \right) = - \left( {V_{{\text{g}}} + u} \right) \cdot \cos \gamma = - V_{{\text{g}}} \cdot \left( {1 + \frac{u}{{V_{{\text{g}}} }}} \right) \cdot \cos \gamma$$

(32)

$$\frac{\partial v}{{\partial \beta }}\left( {\alpha = 80^\circ } \right) = \left( {V_{{\text{g}}} - u} \right) \cdot \cos \gamma = V_{{\text{g}}} \cdot \left( {1 - \frac{u}{{V_{{\text{g}}} }}} \right) \cdot \cos \gamma$$

(33)

$$\frac{\partial u}{{\partial \gamma }}\left( {\alpha = 80} \right) = V_{{\text{a}}} \cdot \sin \gamma \cdot \sin \beta = \left( {V_{{\text{g}}} - u} \right) \cdot tg \gamma = V_{{\text{g}}} \cdot \left( {1 - \frac{u}{{V_{{\text{g}}} }}} \right) \cdot tg \gamma$$

(34)

$$\frac{\partial u}{{\partial \gamma }}\left( {\alpha = 260} \right) = V_{{\text{a}}} \cdot \sin \gamma \cdot \sin \beta = - \left( {V_{{\text{g}}} + u} \right)tg \gamma = - V_{{\text{g}}} \cdot \left( {1 + \frac{u}{{V_{{\text{g}}} }}} \right) \cdot tg \gamma$$

(35)

$$\frac{\partial v}{{\partial \gamma }} = V_{{\text{a}}} \cdot \sin \gamma \cdot \cos \beta = - v \cdot tg\gamma $$

(36)

Considering the flight slopes of ICL aircraft within the dataset (Buzdugan and Stefan 2020), an approximate average value of the aircraft pitch angle of 10° was determined. For this value, tg γ ≃ γ, from which (27) yields the error estimates for the wind components u and v for zonal ICL flights:

$$\delta u\left( {\alpha = 80,\beta , \gamma } \right) = v \cdot \delta \beta + V_{{\text{g}}} \cdot\left( {1 - \frac{u}{{V_{{\text{g}}} }}} \right) \cdot \gamma \cdot \delta \gamma$$

(37)

$$\delta u\left( {\alpha = 260,\beta , \gamma } \right) = v \cdot \delta \beta - V_{{\text{g}}} \cdot \left( {1 + \frac{u}{{V_{{\text{g}}} }}} \right) \cdot \gamma \cdot \delta \gamma$$

(38)

$$\delta v\left( {\alpha = 80 ,\beta , \gamma } \right) = - V_{{\text{g}}} \cdot \delta \alpha + V_{{\text{g}}} \cdot \left( {1 - \frac{u}{{V_{{\text{g}}} }}} \right) \cdot \cos \gamma \cdot \delta \beta - v \cdot \gamma \cdot \delta \gamma$$

(39)

$$\delta v\left( {\alpha = 260 ,\beta , \gamma } \right) = V_{{\text{g}}} \cdot \delta \alpha - V_{{\text{g}}} \cdot \left( {1 + \frac{u}{{V_{{\text{g}}} }}} \right) \cdot \cos \gamma \cdot\delta \beta - v\cdot \gamma \cdot\delta \gamma $$

(40)

Apart from ICL, the pitch angle $\gamma$ is sufficiently small we can approximate cos $\gamma$ = 1 and tg $\gamma$ = 0, so (37)–(40) become the error estimates for u and v components for zonal descending flights:

$$\delta u\left( {\alpha = 80,\beta , \gamma } \right) = \delta u\left( {\alpha = 260,\beta , \gamma } \right) = v \cdot \delta \beta$$

(41)

$$\delta v\left( {\alpha = 80 ,\beta , \gamma } \right) = - V_{{\text{g}}} \cdot\delta \alpha + V_{{\text{g}}} \cdot \left( {1 - \frac{u}{Vg}} \right) \cdot \delta \beta$$

(42)

$$\delta v\left( {\alpha = 260 ,\beta , \gamma } \right) = V_{{\text{g}}} \cdot \delta \alpha - V_{{\text{g}}} \cdot \left( {1 + \frac{u}{{V_{{\text{g}}} }}} \right) \cdot \delta \beta$$

(43)

Appendix 2

The errors of the measured components us and vs depend on the error of the instrument orientation angle against the true north, measured clockwise:

$$\delta u_{{\text{s}}} = V_{{\text{s}}} \cdot \cos \varphi \cdot \delta \varphi$$

(44)

$$\delta v_{{\text{s}}} = V_{{\text{s}}} \cdot \sin \varphi \cdot \delta \varphi$$

(45)

After averaging over the data sample, in zonal winds (φ = 270° and φ = 90°) we get:

$$\overline{{\delta u_{{\text{s}}} }} = 0$$

(46)

$$\overline{{\delta v_{{\text{s}}} }} = \overline{{V_{{\text{s}}} }} \cdot \delta \varphi \quad {\text{for easterly wind}}$$

(47)

$$\overline{{\delta v_{{\text{s}}} }} = - { }\overline{{V_{{\text{s}}} }} \cdot{ }\delta \varphi \quad {\text{for westerly wind}}{.}$$

(48)

Thus, in zonal winds, the measurement error of the u component caused by the instrument orientation error is negligible.

Recalling Fig. 5, we notice that the observed dependence of the v component bias on the wind direction is also compatible with a positive value of the instrument orientation error angle δφ.

If we assign the index “ms” to the Mode-S EHS derived wind, and the index “s” to the remotely sensed wind, and by noting with u and v the true values of the wind components, we have:

$$u_{{{\text{ms}}}} = u + \delta u_{{{\text{ms}}}}$$

(49)

$$u_{{\text{s}}} = u + \delta u_{{\text{s}}}$$

(50)

$$v_{{{\text{ms}}}} = v + \delta v_{{{\text{ms}}}}$$

(51)

$$v_{{\text{s}}} = v + \delta v_{{\text{s}}}$$

(52)

Averaging the subtracted equations corresponding to the same component over the entire dataset, and considering (46), we obtain the following estimates of the mean differences between the Mode-S EHS derived and sodar measured components:

$$\overline{{v_{{{\text{ms}}}} - v_{{\text{s}}} }} = \overline{{\delta v_{{{\text{ms}}}} }} - \overline{{\delta v_{{\text{s}}} }}$$

(53)

$$\overline{{u_{{{\text{ms}}}} - u_{{\text{s}}} }} = \overline{{\delta u_{{{\text{ms}}}} }} $$

(54)