March/April 中国海洋大学 Lecture "Advanced conceptual issues in climate and coastal science" 12 March - Utility of coastal science with emphasis on climate issues 26 March - Concepts of regional climate servicing 2 April – Detection and attribution of change 9 April - Concepts of downscaling

Scaling cascade and climate models

Global climate Formation of the general circulation on an aqua planet from a state of rest (from Fischer et al., 1991)

Risbey and Stone (1996) Long term mean of - zonal wind at 200 hpa, - geopotential, height at 500 hPa, and - band-pass filtered variance of 500 hpa geopotential height („storm track“) caused by planetary scale land-sea contrast and orographic features Continental climate

Composites of air pressure (left) and zonal wind (right) for day before intense precip in the Sacramento Valley (top), on the day of maximum precip (middle) Averaged over the ten most intense precip events. Risbey and Stone (1996) Regional climate

Climate = statistics of weather The genesis of climate C s = f(C l, Φ s ) with C l = larger scale climate C s = smaller scale climate Φ s = physiographic detail at smaller scale

Regional climates do not make up global climate. Instead, regional climate should be understood as the result of an interplay of global climate and regional physiographic detail. The local processes are important for the formation of the global climate not in terms of their details but through their overall statistics. Implications: Planetary scale climate can be modeled with dynamical models with limited spatial resolution The success on planetary scales does not imply success on regional or local scales. The effect of smaller scales can be described summarily through parameterizations.

Dynamical processes in a global atmospheric general circulation model

Climate = statistics of weather The genesis of climate C s = f(C l, Φ s ) with C l = given by global simulations and global re-analyses C s = smaller scale states or statistics Φ s = parameters representative for regional features f =statistical or dynamical model  “downscaling”

Statistical downscaling: Determining statistics of impact variables von Storch, H. and H. Reichardt 1997: A scenario of storm surge statistics for the German Bight at the expected time of doubled atmospheric carbon dioxide concentration. - J. Climate 10,

The case of intra- seasonal storm- related sea level variations in Cuxhaven (at the mouth of the river Elbe ) Annual percentiles of the approximately twice-daily hig-htide water levels at Cuxhaven after subtraction of the linear trend in the annual mean. From top to bottom, 99%, 90%, 80%, 50%, and 10% percentiles. The 90%, 80%, and 50% percentiles. Units are centimeters.

Canonical Correlation Analysis (CCA) The coefficients a s,1 and a q,1 have maximum correlation, the coefficients a s,2 and a q,2 have maximum correlation after subtraction of the 1 st components, and so forth The analysis describes which anomalous monthly mean large- scale pressure anomalies in winter over the North Atlantic are associated with which intra- monthly anomalies of 50%, 80% and 90% percentiles of storm water variations at Cuxhaven One vector time series S t is formed by the coefficients of the first four empirical orthogonal functions (EOFs) of winter [December–February (DJF)] monthly mean air pressure distributions. Prior to the EOF analysis, the air pressure data were centered; that is, the long-term mean distribution was subtracted so that anomalies were obtained. The other vector time series Q t is three- dimensional, featuring the 50%, 80%, and 90% percentiles of winter intra- monthly storm-related water-level distributions: Q = (q 50%, q 80%, q 90% ) The result of a CCA is pairs of vectors (p s;k, p q;k ) and time coefficients a s;k (t) and a q;k (t) so that S t =  k a s,k (t) p s;k And Q t =  k a q,k (t) p q;k

Time series of 90% percentiles of intra- monthly storm-related water-level variations in Cuxhaven, as derived from in situ observations (solid) and estimated from the monthly mean air pressure field (dashed). First two characteristics patterns p s;1 (top) and p s;2 (bottom) of monthly mean air pressure anomalies over the northeast Atlantic. The coefficients of these CCA vectors share a maximum correlation with the coefficients of the water-level percentile patterns given on the right. Units are hPa.

Statistical downscaling: generating time series through conditional weather generators Busuioc, A., and H. von Storch, 2003: Conditional stochastic model for generating daily precipitation time series, Clim. Res. 24,

Rainfall as a 2-state first-order Markov chain A „rainfall generator“ is a stochastic process, which mimics the behavior of rainfall as a sequence of either „wet“ or „dry“ days. A specific rainfall generator makes use of four parameters: a)The probability to have wet day following another wet day Prob(w t |w t-1 ) = p 11 ThenProb(d t |w t-1 ) = 1-p 11 b)The probability to have wet day following a dry day Prob(w t |d t-1 ) = p 01 ThenProb(d t |d t-1 ) = 1-p 01 c)c) The amount of rainfall on a „wet“ day is described by a  -Distribution  (k,β) with „shape“ parameter k and „scale“ parameter β. The four parameters are p 11, p 10, k, and  = kβ (the mean). They can be estimated from the data.

Patterns of the first CCA pair of winter mean SLP and winter parameters of precipitation distribution derived from the first half of the observations (1901–1949)

Winter standardized anomalies of the precipitation distribution parameters for 1901– 1999 derived from observations (solid line) and derived indirectly from the observed European-scale SLP anomalies using the downscaling model (dashed line) fitted to the 1901–1949 data

Dynamical downscaling: Regional models as downscaling tool conventional set-up

Regional atmospheric modelling: nesting into a global state

Regional atmospheric models serve the purpose to describe the dynamics at regional and smaller scales well. Ideally, regional models would return one unique solution given a set of boundary values. However, this is not the case. Mathematically, there is no unique solution for a given set of each boundary values. The problem is not a boundary value / initial value problem. A numerical problem is that the wave propagation velocity depends on grid resolution, so that waves travelling within and outside the limited area will arrive at the outgoing boundary at different times. This problem was solved by introducing the sponge zone, by Hughes Davis, in The sponge-zone does not solve the problem of the non-existence of a well defined solution of the boundary value problem.

Rinke, A., and K. Dethloff, 2000: On the sensitivity of a regional Arctic climate model to initial and boundary conditions. Clim. Res. 14, Ensemble standard deviations of 500 hPa height [m²/s²] When formulated as a boundary value problem, and integrated on a grid, an ensemble of solutions emerges. It is unknown (to me), how this ensemble of solutions look like.

Lateral constraint too weak to maintain large-scale in the interior if flushing time too long (Example: May 1993; strongly non-zonal flow) - Castro and Pielke, 2004)  small -- large integration area In some cases, the kinetic energy in the interior of the nested grid can not be maintained.

Big Brother Experiments Denis, B., R. Laprise, D. Caya and J. Cote, 2002: Downscaling ability of one-way nested regional climate models: The Big brother experiment. Climate Dyn. 18, In Big Brother experiments, a global simulation BB with high resolution is done. A subarea is cut out, and coarsened values of BB at the boundary prescribed; then LAM is run. It turns out that – at least in case of a strongly flushed flow – the small scale dynamical features of BB reappear in the LAM simulation.

Evolution of the specific humidity at 700 hPa during the first 96 hours, sampled every 24 hours. The left column is the control big brother. The inner squares of the right column correspond to the little-brother domain while the area outside these squares are the filtered big- brother humidity used to nest the little brother. Denis, B., R. Laprise, D. Caya and J. Cote, 2002: Downscaling ability of one-way nested regional climate models: The Big brother experiment. Climate Dyn. 18,

Dynamical downscaling: Large scale constraining (spectral nudging)

global model Well resolved Insufficiently resolved Spatial scales variance

Well resolved Insufficiently resolved Spatial scales variance regional model Added value

A mathematically well-posed problem is achieved when the task of describing the dynamics of determining regional and smaller scales is formulated as a state space problem, which is conditioned by large scales. Physically, this means that genesis of regional climate is better framed as a downscaling problem and not as a boundary value problem.

RCM Physiographic detail 3-d vector of state Known large scale state projection of full state on large-scale scale Large-scale (spectral) nudging

Expected added value Statistics and events on scales, which are not well resolved for the global system, but sufficiently resolved for the regional model. In particular, increased variance on smaller scales. No improvement of the dynamics and events on scales, which are already well done by the global system

Useful quantities to check 1.Similarity of large-scale state 2.Unchanged variance of large scales 3.Dissimilarity of regional scales 4.Increased variance on regional scales 5.Distributions of quantities in physiographic complex regions 6.Extremes 7.Regional dynamical features, such as polar lows, tropical storms, medicanes

Pattern correlation coefficients for zonal wind at 500 hPa between the global reanalyses and the RCM with standard forcing via the lateral boundaries and the RCM with spectral nudging Northern Europe global regional Nudging of the large scales

34 Europe simulation with REMO, 0.5 o (Feser, 2006) Positive values show added value of the regional model. 95% significant deviations are marked by a *. PCC DWD and NCEP PCC improvement/ deterioration REMO Nudge PCC improvement/ deterioration REMO Standard Pattern correlation coefficients [PCC, %]

Improved presentation of in coastal regions ERA-I-driven multidecadal simulation with RCM CCLM over East Asia ( 李德磊, 2015) Grid resolution: 0.06 o Employing spectral nudging (wind above 850 hPa, for scales > 800 km) Usage of Quikscat-windfields (QS) over sea as a reference Considering ratios  2 QS :  2 ERA and  2 QS :  2 RCM Determining Brier Skill score for all marine grid boxes B = 1 – (RCM-QS) 2 / (ERA-QS) 2

QuikSCAT/ ERA I-reanalysis Quikscat/ CCLM regional simulation 李德磊, 2015

QuikSCAT: Added Value – Brier skill score vs. ERA Open Ocean: No value added by dynamical downscaling Coastal region: Added Value in complex coastal areas 李德磊, 2015

Comparison of CCLM (left-panel, y-axis) and ERA-I (right-panel, y-axis) widn data with observations from two coastal stations and two offshore wind observations (x- axis). Scatter plots (grey dots), qq-plots and several statistical measures ( 李德磊, 2015) Coastal stations Offshore stations

Improved representation of sub-synoptic phenomena NCEP-driven multidecadal simulation with RCM CLM over North Pacific ( 陈飞 et al., 2012, 2013, 2014) Grid resolution: about 0.4 o Employing spectral nudging (wind above 850 hPa, for scales > 800 km) Simulation of sub-synoptic phenomena Polar lows in the Northern North Pacific

North Pacific Polar Low on 7 March 1977 NOAA-5 infrared satellite image at 09:58UTC 7th March 1977 North Pacific Polar Lows ( 陈飞 et al., 2012, 2013 and 2014)

Annual frequency of past polar lows in the North Pacific 陈飞 et al., 2013 Number of detected Polar Lows in the North Pacific per Polar Low season (PLS; October to April). The trend from 62 PLSs, from 1948/1949 to 2009/2010, amounts to 0.17 cases/year.

Scenarios of Polar Low Formation in the North Pacific A1B_1: A1B_2: A1B_3: A1B_1: A2_1: 陈飞 et al., 2014

Improved representation of forcing fields for impact models NCEP-driven multidecadal simulation with RCM REMO in Europe Grid resolution: 0.5 o Employing spectral nudging (wind above 850 hPa, for scales > 800 km) simulation Wind and air pressure used to drive models of sea level and circulation of marginal seas (not shown) for describing currents and sea level Wind used to drive models of the statistics of surface waves (ocean waves) in coastal seas (North Sea).

Weisse, pers. comm. January 1980-January 1997 Extreme value analysis of wind speed at platform K13 (southern North Sea) simulated observed

simuliert Extreme wind events simulated compared to local observations Weisse, pers. comm.

Red: buoy, yellow: radar, blue: wave model run with REMO winds wave direction significant wave height [days] Gerd Gayer, pers. comm., 2001

Yantai, 18 June 2007Page 47 wind waves Changing significant wave height, Weisse, pers. comm.

The CoastDat-effort at the Institute for Coastal  Long-term, high-resolution reconstructions (60 years) of present and recent developments of weather related phenomena in coastal regions as well as scenarios of future developments (100 years)  Northeast Atlantic and northern Europe.  Assessment of changes in storms, ocean waves, storm surges, currents and regional transport of anthropogenic substances.  Extension to other regions and to ecological parameters. Applications  many authorities with responsibilities for different aspects of the German coasts  economic applications by engineering companies (off-shore wind potentials and risks) and shipbuilding company  Public information Integration area used in HZG reconstruction and regional scenarios

Wave Energy Flux [kW/m] Currents Power [W/m 2 ] Some applications of - Ship design - Navigational safety - Offshore wind - Interpretation of measurements - Oils spill risk and chronic oil pollution - Ocean energy - Scenarios of storm surge conditions - Scenarios of future wave conditions Weisse, pers. comm.

Conclusion … Downscaling (C s = f(C l,Φ s )) works with respect to atmospheric dynamics – ocean dynamics: needs more analysis. Several options, - statistical downscaling, generating characteristics of distributions and processes, such as monthly means, intra- monthly percentiles, parameters of Markov processes etc. - dynamical downscaling using „state-space“ formulation of large- scale constraining (spectral nudging) Added value on - medium scales (in particular coastal regions and medium scale phenomena (in particular storms) - in generating regional impact variables, in particular wind for storm surges and ocean waves. Downscaling allows the generation of homogeneous data sets (i.e., data sets of uniform quality across many decades of years)